Quadratic Equation SolverEvery step, from factoring to the quadratic formula.

Type any quadratic equation such as 2x² + 3x − 2 = 0 and get the roots with each step explained.
Exact answers with square roots, complex roots when there are no real ones, and a decimal value.

Factoring or formulaExact rootsComplex solutions

No sign-up Unlimited use Remembers your numbers

Calculated on your device. What you type is not sent anywhere.

THREE SIMPLE STEPS

How to use the Quadratic Equation Solver

Type the equation

Write it as you see it, for example x^2 - 5x + 6 = 0 or 3x^2 = 2x + 8. It does not need to be in standard form.

Press Solve

The solver puts it in standard form, then factors it or uses the quadratic formula with the discriminant.

Read the roots

See both solutions exactly and as decimals, with every step and a check that they satisfy the equation.

WaveSpeed AI

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Pay as you go

$1 in free credits for eligible new accounts. No card needed. Generators have separate account and credit requirements. The math solver is free.

Quadratic Equation Solver FAQ

How does it solve a quadratic equation?

It moves everything to one side to get ax² + bx + c = 0. If the discriminant is a perfect square it factors the quadratic and uses the zero product property; otherwise it uses the quadratic formula x = (−b ± √(b² − 4ac))/2a and simplifies the roots.

What if the discriminant is negative?

Then there are no real solutions. The solver shows the two complex solutions, such as x = −1 ± 2i, and says that there are no real roots.

Does it give exact answers?

Yes. Roots stay exact with square roots and fractions, for example (−1 + √5)/2, and a decimal value is shown as well.

Can it solve other equations too?

Yes. The same solver handles linear, cubic and higher polynomial equations, rational equations, equations with roots, exponentials, logarithms and trig functions, and systems of equations.

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