Quadratic Equation Solver
How to Use
Enter the coefficients of the quadratic equation ax² + bx + c = 0
Example: For x² - 5x + 6 = 0, enter a=1, b=-5, c=6
About This Calculator
Quadratic Equation Solver is designed to reduce manual errors and give repeatable outputs when you need quick, reliable answers.
Solve quadratic equations and return real or complex roots to support algebra practice, exam prep, and model validation.
If your workflow expands, pair this calculator with Factorization Calculator and Simultaneous Equations Solver to cross-check assumptions and build a stronger analysis chain.
Formula
For ax^2 + bx + c = 0: x = [-b ± sqrt(b^2 - 4ac)] / (2a)
Example Calculation
The worked example below demonstrates how the input fields translate into the final output. Use it as a quick validation pass before entering your own numbers.
- a: 1
- b: -5
- c: 6
Explanation of Results
Result Interpretation
A positive discriminant indicates two distinct real roots, so the parabola crosses the x-axis at two points.
FAQ
What does the discriminant tell me?
If b^2 - 4ac is positive, there are two real roots; zero gives one repeated root; negative gives complex conjugates.
Can I use decimal coefficients?
Yes. Decimal coefficients are supported, which helps with applied modeling problems.
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