Quadratic Equation Solver

⚡ Solve any quadratic equation instantly. Get real or complex roots with discriminant, vertex, and step-by-step solutions. 100% free.

x² - 5x + 6 = 0

Coefficient a

Coefficient b

Coefficient c

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The Best Quadratic Equation Solver

Our quadratic equation solver is designed for students who want to actually understand math. Solve ANY quadratic equation (ax² + bx + c = 0) and get both real and complex roots with detailed step-by-step solutions. We also show you the discriminant and vertex! Perfect for algebra homework, physics problems, and understanding parabolas. No signup, no ads, just instant accurate results.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

The universal solution

Discriminant

D = b² - 4ac

Determines nature of roots

Vertex

h = -b/(2a), k = f(h)

Peak/valley point

Examples

x² - 5x + 6 = 0

1a=1, b=-5, c=6

2D = 25 - 24 = 1

3x = (5 ± 1) / 2

4x = 3 or x = 2

x² + 4x + 4 = 0

1D = 16 - 16 = 0

2One repeated root

3x = -4/2 = -2

Frequently Asked Questions

Is this quadratic solver free?

Yes! 100% free with no signup required and no ads.

What does the discriminant tell us?

The discriminant (b² - 4ac) reveals the nature of roots: positive means two real roots, zero means one repeated root, negative means two complex roots.

Why are there two solutions?

A parabola can cross the x-axis at most twice, giving up to two solutions. The ± in the formula accounts for both intersection points.