Quadratic Equation Solver

Solve ax² + bx + c = 0 — get roots, discriminant, vertex & steps

ax² + bx + c = 0
x² +
x +
= 0

Results

How to Use

  1. Enter the coefficients a, b, and c from your equation ax² + bx + c = 0.
  2. Click Solve or press Enter to calculate.
  3. View the roots, discriminant, vertex, axis of symmetry, and step-by-step solution.
  4. The graph shows the parabola with roots marked on the x-axis.
  5. Use the example buttons to try common equations instantly.

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Frequently Asked Questions

What is a quadratic equation?

A quadratic equation is a second-degree polynomial in the form ax²+bx+c=0, where a≠0. It can have two real roots, one repeated root, or two complex roots.

What is the quadratic formula?

The quadratic formula is x = (-b ± √(b²-4ac)) / (2a). It solves any quadratic equation.

What is the discriminant?

The discriminant D = b²-4ac. D>0: two real roots. D=0: one repeated root. D<0: two complex roots.

How do I find the vertex?

The vertex is at x = -b/(2a), y = c - b²/(4a). It's the max or min point of the parabola.

Can it solve complex roots?

Yes! When D<0, both complex conjugate roots are shown in a+bi form.

What if a=0?

If a=0, it becomes a linear equation bx+c=0, solved as x = -c/b.

Is it free?

Yes, completely free. No signup required.

Does it show steps?

Yes, the discriminant calculation and formula substitution are shown step by step.