Enter coefficients a, b, and c.
Algebra Calculator
Quadratic Equation Solver
Solve ax² + bx + c = 0, classify the discriminant, and return real or complex roots.
Instant answer
Formula breakdown
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Enter your values
Use the example values or replace them with your own. Required validation happens before the calculation.
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Calculated answer
Result
Simple workflow
How to use the Quadratic Equation Solver
Follow these steps to get a reliable result and understand how it was produced.
Calculate the discriminant b²−4ac.
Apply the quadratic formula and classify the roots.
Understanding the calculation
The discriminant Δ = b²−4ac determines whether there are two real roots, one repeated root, or a complex-conjugate pair.
x = (−b ± √(b²−4ac)) / 2aThe result panel substitutes your numbers into this relationship and shows the important intermediate values.
Common uses
- Algebra and graph intersections
- Projectile and optimisation problems
- Factoring checks
Accuracy tips
- Coefficient a cannot be zero.
- A negative discriminant produces complex roots.
- The sum of roots is −b/a and the product is c/a.
Helpful answers
Quadratic Equation Solver FAQs
Important details about formulas, inputs, limitations, and result interpretation.
What does the discriminant tell me?
Positive means two real roots, zero means one repeated real root, and negative means two complex roots.
Can this solve a linear equation?
Use the Linear Equation Solver when a is zero.
Why are complex roots shown with i?
i represents √−1, allowing solutions when the discriminant is negative.
Are repeated roots listed twice?
The calculator identifies the single repeated value and its root type.