Quadratic Solver

Solve any quadratic equation ax² + bx + c = 0 for its real roots using the quadratic formula. It handles linear cases and flags complex roots via the discriminant.

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💡 Good to know: The discriminant b²−4ac predicts the answer before you solve: positive gives two real roots, zero one, negative two complex ones.

Worked example

x₁: 2 · x₂: 1

How it’s solved

Worked on the example above, step by step — follow along and you can do it on paper next time, no tool required.

The quadratic formula solves ax² + bx + c = 0. The discriminant b² − 4ac decides how many real roots there are.
Compute the discriminant b² − 4ac
(-3)² − 4×1×2 = 1
Plug into (−b ± √D) ÷ 2a
(3 ± √1) ÷ 2
Evaluate the + and − branches
x₁ = 2, x₂ = 1

Learn the method

Inputs

a
1
b
-3
c
2

Frequently asked

What are the roots of x² − 3x + 2?

x₁ = 2 and x₂ = 1.

What if there are no real roots?

A negative discriminant means the roots are complex — the tool says so and shows the discriminant.