Quadratic Equation Solver

Solve quadratic equations instantly. Free online quadratic formula calculator with real and complex solutions.

The Quadratic Equation Solver finds the roots of any quadratic equation in the form ax² + bx + c = 0. Using the quadratic formula, this calculator handles all cases including two real roots, one repeated root, and complex conjugate pairs. Essential for algebra students, engineers, and anyone working with parabolic relationships. See the discriminant, solutions, and step-by-step work.

Common use cases

  • Algebra homework and tests
  • Physics projectile calculations
  • Engineering design problems
  • Financial break-even analysis
  • Optimization problems

How to use

  1. Enter coefficient a (x² term)
  2. Enter coefficient b (x term)
  3. Enter coefficient c (constant)
  4. Click solve for the roots
  5. View discriminant and solution type

FAQ

What is the quadratic formula?

x = (-b ± √(b²-4ac)) / 2a, giving both solutions to ax² + bx + c = 0.

What is the discriminant?

b²-4ac determines solution types: positive = 2 real roots, zero = 1 repeated root, negative = 2 complex roots.

Can this solve equations not equal to zero?

Rearrange your equation to = 0 form first, then enter the coefficients.

What if a = 0?

Then it's not quadratic—it's linear (bx + c = 0, solved as x = -c/b).