Quadratic Equation Solver

Solve ax² + bx + c = 0 with discriminant and complex roots. Solve quadratic equations with step-by-step working. Real or complex roots, discriminant explained and vertex shown. Free quadratic formula calculator.

This tool runs 100% in your browser. Your input is never sent to any server — you can even go offline after the page loads.

About the Quadratic Equation Solver

Every quadratic equation ax² + bx + c = 0 can be solved with one formula — but substituting correctly and interpreting the discriminant is where marks are lost. Enter a, b and c and this solver computes both roots using the quadratic formula, classifies them via the discriminant (two real, one repeated, or a complex conjugate pair), shows the vertex of the corresponding parabola, and lists the steps so you can follow the working, not just the answer.

How to use the Quadratic Equation Solver

  1. Enter the coefficients a, b and c.
  2. The roots appear instantly.
  3. Check the discriminant explanation.
  4. Follow the steps for your homework write-up.

Key features

What does the discriminant tell me?
b² − 4ac decides everything: positive means two distinct real roots, zero means one repeated root, and negative means a pair of complex conjugate roots.
What if a is zero?
Then the equation is linear (bx + c = 0), not quadratic, and has a single root −c/b — the solver handles this case automatically.

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