Solve Equation Calculator

One equation · two clear sides

Enter the equation, then choose how to answer

Type one expression on each side of the fixed equals sign. Linear and quadratic equations in x are simplified locally, with the selected method and every supported step kept visible.

Solve for xx = -1 or x = 2

Find every supported value of x that makes both sides equal.

Degree 2

Entered equation

3x^(2) - 5x = 6 - 2x

Interpreted equation

3x^2 − 5x = -2x + 6

Standard form

3x^2 − 3x − 6 = 0

a: 3
b: -3
c: -6
Discriminant Δ: 81
Roots / solutions: x = -1 or x = 2
Real factorization: 3(x + 1)(x − 2)

Method shown in full

Calculation steps

Simplify both sides3x^2 − 5x = -2x + 6
Expand products and powers on each side, then combine like terms.
Write standard form3x^2 − 3x − 6 = 0
Subtract the right side from both sides so every term is on the left.
Calculate the discriminantD = (-3)^2 − 4(3)(-6) = 81
The sign of D determines whether the roots are distinct real, repeated, or complex.
Apply the quadratic formulax = (3 ± √81) / 6
Substitute a, b, and c into x = (−b ± √D) / (2a).
Evaluate both rootsx = -1 or x = 2
Use the plus and minus branches of the square root.

Supported scope is one variable x and polynomial equations through degree two. Unsupported notation is reported instead of being interpreted as a different problem.

Two-sided equation workbench

Move both sides into standard form, then choose how to answer

A clear equation editor keeps the left and right expressions separate, then uses equivalent operations to build standard form. From there the degree determines whether linear isolation, factoring, or the quadratic formula supplies the roots.

Step-by-step guide · Two-sided equation workbench

The review equation supports every quadratic answer view

Accepted equations: one variable x, degree 0–2
Equation layout: left expression = right expression
Answer views: standard form, roots, factors, D, evaluation

Write standard form
Subtract 6−2x from both sides and combine like terms: 3x²−3x−6=0. Therefore a=3, b=−3, and c=−6.
Calculate the discriminant
D=(−3)²−4(3)(−6)=9+72=81. A positive perfect-square discriminant predicts two distinct real roots and a real linear factorization.
Solve and verify both roots
The quadratic formula gives x=(3±√81)/6, so x=−1 or x=2. Equivalently, 3x²−3x−6=3(x+1)(x−2). Substituting either value makes the two original sides equal.

Move both sides into standard form, then choose how to answer: For 3x²−5x=6−2x, the left and right sides can be typed exactly where they appear. Each answer method begins from the same normalized equation.

Separate inputs make the equality structure explicit

Enter one complete expression on each side of the fixed equals sign. The calculator expands supported parentheses and whole-number powers, combines like terms on each side, and then subtracts the right expression from both sides. The resulting standard form preserves the original solution set because the same quantity was removed from both sides.

A linear standard form bx+c=0 isolates one value unless the x coefficient vanishes, in which case the equation is an identity or contradiction. A quadratic standard form ax²+bx+c=0 uses the discriminant D=b²−4ac to classify two real roots, one repeated root, or a complex-conjugate pair. The method menu changes which part of this same calculation is foregrounded.

The review equation supports every quadratic answer view

For 3x²−5x=6−2x, the left and right sides can be typed exactly where they appear. Each answer method begins from the same normalized equation.

Write standard form
Subtract 6−2x from both sides and combine like terms: 3x²−3x−6=0. Therefore a=3, b=−3, and c=−6.
Calculate the discriminant
D=(−3)²−4(3)(−6)=9+72=81. A positive perfect-square discriminant predicts two distinct real roots and a real linear factorization.
Solve and verify both roots
The quadratic formula gives x=(3±√81)/6, so x=−1 or x=2. Equivalently, 3x²−3x−6=3(x+1)(x−2). Substituting either value makes the two original sides equal.

Choose the answer view that matches the question

Standard form and discriminant

Standard form exposes a, b, and c. The discriminant then classifies the roots before any square root is evaluated, which is useful when a question asks for structure rather than only values of x.

Factoring and roots

Factoring rewrites a supported real polynomial as a product. Solving by factoring adds the zero-product property, while Find the Roots reports the x-values directly. A negative discriminant has no real linear factorization even though complex roots still exist.

Evaluation at a chosen x

Evaluation substitutes one declared x value into both original expressions and compares the two numerical results. Agreement verifies that particular candidate; it does not by itself prove that no other solutions exist.

Check the method against the original equation

Keep each entered side intact until the displayed interpreted equation matches the source problem.
Use the x² or xⁿ shortcut to make the exponent explicit; N must be a nonnegative whole number in this bounded polynomial grammar.
Substitute every reported root into both original sides, especially after decimal arithmetic or a repeated root.
Use the algebra calculator for polynomial simplification or finite products beyond this equation workflow, or the quadratic formula calculator when a, b, and c are already known and coefficient entry is preferable.
Use the system of equations calculator when a second variable or a second simultaneous constraint appears. Inequalities, radicals, variable denominators, and arbitrary functions are outside this page rather than silently approximated.

Important limitations

Direct solving is limited to one variable x and polynomial equations through degree two. Simplification accepts finite numeric coefficients, arithmetic, parentheses, implicit multiplication, and nonnegative whole-number powers; inequalities, additional variables, variable denominators, radicals, named functions, and arbitrary LaTeX are rejected instead of guessed.

This formula passed its registered engineering tests and is published under an explicit site-owner policy authorization. No independent expert, QA, editorial, legal, or third-party review is claimed. Verify consequential results with a qualified professional.

Two-sided equation workbench

Move both sides into standard form, then choose how to answer

Step-by-step guide · Two-sided equation workbench

The review equation supports every quadratic answer view

Accepted equations: one variable x, degree 0–2
Equation layout: left expression = right expression
Answer views: standard form, roots, factors, D, evaluation

Write standard form
Subtract 6−2x from both sides and combine like terms: 3x²−3x−6=0. Therefore a=3, b=−3, and c=−6.
Calculate the discriminant
D=(−3)²−4(3)(−6)=9+72=81. A positive perfect-square discriminant predicts two distinct real roots and a real linear factorization.
Solve and verify both roots
The quadratic formula gives x=(3±√81)/6, so x=−1 or x=2. Equivalently, 3x²−3x−6=3(x+1)(x−2). Substituting either value makes the two original sides equal.

Separate inputs make the equality structure explicit

The review equation supports every quadratic answer view

For 3x²−5x=6−2x, the left and right sides can be typed exactly where they appear. Each answer method begins from the same normalized equation.

Write standard form
Subtract 6−2x from both sides and combine like terms: 3x²−3x−6=0. Therefore a=3, b=−3, and c=−6.
Calculate the discriminant
D=(−3)²−4(3)(−6)=9+72=81. A positive perfect-square discriminant predicts two distinct real roots and a real linear factorization.
Solve and verify both roots
The quadratic formula gives x=(3±√81)/6, so x=−1 or x=2. Equivalently, 3x²−3x−6=3(x+1)(x−2). Substituting either value makes the two original sides equal.

Choose the answer view that matches the question

Standard form and discriminant

Standard form exposes a, b, and c. The discriminant then classifies the roots before any square root is evaluated, which is useful when a question asks for structure rather than only values of x.

Factoring and roots

Evaluation at a chosen x

Check the method against the original equation

Keep each entered side intact until the displayed interpreted equation matches the source problem.
Use the x² or xⁿ shortcut to make the exponent explicit; N must be a nonnegative whole number in this bounded polynomial grammar.
Substitute every reported root into both original sides, especially after decimal arithmetic or a repeated root.
Use the algebra calculator for polynomial simplification or finite products beyond this equation workflow, or the quadratic formula calculator when a, b, and c are already known and coefficient entry is preferable.
Use the system of equations calculator when a second variable or a second simultaneous constraint appears. Inequalities, radicals, variable denominators, and arbitrary functions are outside this page rather than silently approximated.

Write standard form

Calculate the discriminant

Solve and verify both roots

Separate inputs make the equality structure explicit

The review equation supports every quadratic answer view

Choose the answer view that matches the question

Standard form and discriminant

Factoring and roots

Evaluation at a chosen x

Check the method against the original equation

Important limitations

Write standard form

Calculate the discriminant

Solve and verify both roots

Separate inputs make the equality structure explicit

The review equation supports every quadratic answer view

Choose the answer view that matches the question

Standard form and discriminant

Factoring and roots

Evaluation at a chosen x

Check the method against the original equation