Quadratic Formula Calculator

Solve quadratic equations using the quadratic formula.

Solve a quadratic equation of the form ax² + bx + c = 0

How to Do It Manually

A quadratic equation has the form ax² + bx + c = 0. Use the quadratic formula to find the values of x that satisfy it.

x = (−b ± √(b² − 4ac)) / 2a
  1. Identify a, b, and c from the equation ax² + bx + c = 0.
  2. Calculate the discriminant: D = b² − 4ac.
  3. If D > 0: two real solutions. If D = 0: one real solution. If D < 0: no real solutions (complex roots).
  4. Apply the formula: x = (−b ± √D) / 2a.

Frequently Asked Questions

What is the discriminant?

The discriminant (b² − 4ac) tells you how many real solutions exist. Positive = 2 solutions, Zero = 1 solution, Negative = no real solutions.