Quadratic Equation Solver
A quadratic equation is an equation in which the highest power of the variable is 2. Its standard form is ax² + bx + c = 0.
Enter a quadratic equal to zero, or any quadratic equation. The solver rewrites it in standard form before applying the formula.
Solve a problem
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Example problems
How this solver works
- Rewrite as ax² + bx + c = 0.
- Compute Δ = b² − 4ac.
- Apply x = (−b ± √Δ) / (2a).
- Substitute each root back into the original equation.
Formula
The quadratic formula. Δ = b² − 4ac determines the number of real roots.
Worked examples
x^2 - 5x + 6 = 0
- a = 1, b = -5, c = 6
- Δ = 25 - 24 = 1
- x = (5 ± 1)/2
- x = 3 or x = 2
Answer: x = 2, x = 3
Common mistakes
Dropping the ±
The square root step produces two candidates unless the discriminant is zero.
Wrong sign on b
If the equation is x² − 5x + 6 = 0, then b is −5, not 5.
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Frequently asked questions
What is a quadratic equation?
An equation whose highest power of the variable is 2. Standard form is ax² + bx + c = 0 with a ≠ 0.
When should I factor instead of using the formula?
Factor when the numbers are friendly. The formula always works and is what this solver uses for verification.
What if the discriminant is negative?
There are no real roots. The solver reports a complex conjugate pair.