How do I solve a quadratic equation?

Use the quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the root, b² − 4ac, is the discriminant. If it is positive there are two real roots, if zero there is one repeated root, and if negative the two roots are complex. The solver computes all of this from your a, b and c.

What does the discriminant tell me?

The discriminant, b² − 4ac, decides the nature of the roots before you find them. Positive means two distinct real roots, zero means a single repeated real root, and negative means two complex roots. The solver shows its value and labels the result so the reason is clear.

Can it handle complex roots?

Yes. When the discriminant is negative, the quadratic has no real roots, but it does have a pair of complex conjugate roots like −1 + 2i and −1 − 2i. The solver works these out and shows them rather than just saying there is no solution.

Equation Solver

Solve linear equations of the form ax + b = 0 and quadratic equations of the form ax² + bx + c = 0. Enter the coefficients and read the roots, including complex roots when the quadratic has none on the real number line. A free equation solver that runs in your browser.

Solve a linear equation like ax + b = 0 or a quadratic like ax² + bx + c = 0 by entering the coefficients. You get the roots, and for a quadratic the discriminant and the complex roots when the parabola never crosses zero. It covers how to solve for x in both the straight-line and the parabola case.

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Read the guide: How to Solve a Quadratic Equation

abc

Two real roots

x = 3 x = 2

Discriminant b²−4ac

Nature

Two real roots

Vertex x

2.5

How to use it

1
Pick linear or quadratic

Choose the equation type. Linear has the form ax + b = 0; quadratic has the form ax² + bx + c = 0.
2
Enter the coefficients

Type the values of a, b and c. The solver computes the answer as you type.
3
Read the roots

See the solution. For a quadratic, you also see the discriminant and whether the roots are real or complex.

When it comes in handy

Algebra homework

Solve a quadratic and check the roots, with the discriminant shown so you understand why there are two, one or none on the real line.

Quick root finding

Find where a straight line or a parabola crosses zero without working through the formula by hand.

Checking the formula

Confirm an answer from the quadratic formula, including the complex case, where mistakes are common.

Instant, exact & 100% in your browser

The maths runs right here in your browser, with fractions and whole numbers kept exact rather than rounded along the way. Nothing you type is sent to a server, there is no sign-up and no limit, and once the page has loaded it keeps working even with no connection.

Frequently asked questions

How do I solve a quadratic equation?: Use the quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the root, b² − 4ac, is the discriminant. If it is positive there are two real roots, if zero there is one repeated root, and if negative the two roots are complex. The solver computes all of this from your a, b and c.
What does the discriminant tell me?: The discriminant, b² − 4ac, decides the nature of the roots before you find them. Positive means two distinct real roots, zero means a single repeated real root, and negative means two complex roots. The solver shows its value and labels the result so the reason is clear.
Can it handle complex roots?: Yes. When the discriminant is negative, the quadratic has no real roots, but it does have a pair of complex conjugate roots like −1 + 2i and −1 − 2i. The solver works these out and shows them rather than just saying there is no solution.

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How to use it

Pick linear or quadratic

Enter the coefficients

Read the roots