Quadratic Equation Calculator
Solve any quadratic equation for its roots using the quadratic formula, showing real or complex solutions, free right in your browser.
Enter Values
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How to use this calculator
- Enter the coefficients a, b and c from ax² + bx + c = 0.
- Press Calculate for the roots.
How it works
The roots are x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the square root (the discriminant) tells you how many real roots there are: positive gives two, zero gives one, negative gives none.
Worked example
x² − 3x + 2 = 0. Discriminant = 1, so x = 2 and x = 1.
Common mistakes
- Entering the coefficients in the wrong order (a, b, c).
- Forgetting a can't be zero, or that a negative discriminant gives complex roots.
Frequently asked questions
What's the quadratic formula?
x = (−b ± √(b² − 4ac)) ÷ 2a. The ± gives the two roots.
What does the discriminant tell me?
b² − 4ac: positive = two real roots, zero = one repeated root, negative = two complex roots.
What if there are no real roots?
A negative discriminant means the solutions are complex numbers, which this calculator doesn't show.
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Cite this tool
Zerdly. (2026). Quadratic Equation Calculator. Retrieved from https://www.zerdly.com/tools/quadratic-equation-calculator/
Tip: Enter any known values to calculate the remaining results.
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