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Quadratic Equation Solver

Calculators Free Updated 21 Sep 2026
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ⓘ About this tool 🔄 Last updated 21 Sep 2026 ✓ Reviewed by TopToolAI Team

Enter a, b and c from ax² + bx + c = 0. You get the roots (real or complex), the discriminant, the vertex and which way the parabola opens, with the quadratic formula worked through.

How to use Quadratic Equation Solver

Step-by-step guide to the boxes below. Open it only if you need help.

  1. 1
    a Text

    The number in front of x squared. It cannot be 0.

    Example: 1

  2. 2
    b Text

    The number in front of x. Use 0 if there is no x term.

    Example: -3

  3. 3
    c Text

    The plain number without x. Use 0 if there is none.

    Example: 2

  4. 4
    Press “Solve”

    Click the button under the boxes. If something is missing or not valid, a short message tells you which box to fix.

  5. 5
    Read your result

    Your answer appears under the button, with a short note in plain words where it helps. Change any box and press again to compare different numbers.

Solve ax² + bx + c = 0

Embed this calculator on your website

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Quadratic Equation Solver FAQs

What does the discriminant tell me?
Positive means two real roots, zero means one repeated root, and negative means the roots are complex.
What if a is 0?
Then it is not quadratic any more. The tool solves it as the linear equation bx + c = 0.
Does it do complex roots?
Yes. They show up as p ± qi when the discriminant is negative.
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) ÷ 2a. It gives the roots of ax² + bx + c = 0.

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