Quadratic Equation Solver

Solve any quadratic equation ax² + bx + c = 0 instantly using the quadratic formula.

▼ Enter coefficients for ax² + bx + c = 0, then click Calculate
ax2 + bx + c = 0
Roots
Discriminant (b² - 4ac)
x₁
x₂
Vertex

Solving Quadratic Equations

This tool solves any quadratic equation in the form ax² + bx + c = 0 using the quadratic formula, showing both real roots (or complex roots, when the discriminant is negative) — useful for algebra homework or quickly checking a hand-solved equation.

Example: for x² − 3x + 2 = 0 (a=1, b=−3, c=2), the roots are x = 1 and x = 2 — enter your own a, b, and c values above.

The Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a. The discriminant (b² - 4ac) determines the nature of the roots: positive gives two real roots, zero gives one repeated real root, and negative gives two complex roots.

Frequently Asked Questions

It solves any quadratic equation in the form ax^2 + bx + c = 0 instantly using the quadratic formula.

x = (-b +/- the square root of (b^2 - 4ac)) / 2a.

The discriminant (b^2 - 4ac) determines the nature of the roots: positive gives two real roots, zero gives one repeated real root, and negative gives two complex roots.

Yes — when the discriminant (b² - 4ac) is negative, the calculator returns the two complex roots in the form a + bi, rather than showing an error.

You need the coefficients a, b, and c from the equation ax^2 + bx + c = 0.

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