Quadratic Equation Calculator
Solve any quadratic equation ax² + bx + c = 0, including real and complex roots.
Reviewed October 7, 2026 Runs in your browser — inputs are never stored
Solve ax² + bx + c = 0
Two real roots
x₁ = 2
x₂ = 1
Discriminant = 1
This tool performs standard mathematical operations for educational and reference purposes. Always double-check results for critical academic or professional work.
About the Quadratic Equation Calculator
The quadratic equation calculator solves equations of the form ax² + bx + c = 0 with the quadratic formula, x = (−b ± √(b² − 4ac)) / 2a. It also shows the discriminant, b² − 4ac, which tells you what kind of roots to expect: a positive discriminant gives two real roots, zero gives one repeated root, and a negative value gives two complex roots, which the calculator shows in a + bi form.
How to use it
- 1Rearrange your equation so that one side equals zero.
- 2Enter the coefficients a, b and c (a cannot be zero).
- 3Press Calculate to see the discriminant and the roots.
Worked example
x² − 3x + 2 = 0 has a = 1, b = −3 and c = 2. The discriminant is 9 − 8 = 1, so there are two real roots: x = (3 ± 1) ÷ 2, giving x = 2 and x = 1.
How it works
Formula
x = (−b ± √(b² − 4ac)) / 2a
Discriminant
b² − 4ac determines the roots: positive gives two real roots, zero gives one, negative gives two complex roots.
Who it is for
Algebra students, teachers and anyone solving projectile or area problems.
Why it helps
It handles the sign errors that commonly creep into the quadratic formula and also gives complex roots.
Common use cases
- Checking algebra homework
- Finding where a parabola crosses the x-axis
- Solving physics problems involving projectile height
Frequently asked questions
A:The value b² − 4ac, which tells you how many real solutions the equation has.
A:Yes, when the discriminant is negative it reports the complex conjugate roots.
Reviewed for accuracy · Last updated October 7, 2026
Calculations use standard, well-established mathematical identities and algorithms with no approximation beyond normal floating-point precision.
CalcWisee Editorial Team
Calculator development and formula review
CalcWisee is an independent site founded by Ayman. Every calculator is built from a published formula or official definition, tested against hand-worked examples before it goes live, and corrected promptly when a reader reports an issue to ayman@calcwisee.com.
Expertise: Financial mathematics, Health and fitness formulas, Applied mathematics, Unit conversion standards
References & sources
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