Quadratic Formula Solver
Enter values for a, b, and c in the equation ax² + bx + c = 0.
Current equation: x² + 0x + 0 = 0
What this solving quadratic formula calculator does
This calculator solves any quadratic equation in standard form: ax² + bx + c = 0. It uses the quadratic formula to find the roots (solutions): x = (-b ± √(b² - 4ac)) / 2a.
You can use it as a quick quadratic equation solver for homework, test prep, engineering calculations, and algebra practice. It handles both real roots and complex roots.
How to use the calculator
Step-by-step
- Enter your coefficient values for a, b, and c.
- Make sure a ≠ 0 (otherwise the equation is linear, not quadratic).
- Click Calculate Roots.
- Read the discriminant, the type of roots, and the final solutions.
Why the discriminant matters
The discriminant is D = b² - 4ac. It tells you what kind of roots you have:
- D > 0: Two distinct real roots.
- D = 0: One repeated real root (double root).
- D < 0: Two complex conjugate roots.
Quick example
For x² - 3x + 2 = 0, we have a = 1, b = -3, c = 2. The discriminant is (-3)² - 4(1)(2) = 9 - 8 = 1, so there are two real roots. Substituting into the formula gives x = 2 and x = 1.
Common mistakes when solving quadratics
- Forgetting that b includes its sign (for example, -5 is not 5).
- Dropping parentheses when substituting values into b² - 4ac.
- Using 2a incorrectly as 2 + a instead of 2 × a.
- Assuming negative discriminants mean “no solution” (they have complex solutions).
When to use this tool
This quadratic formula calculator is useful for:
- Algebra and pre-calculus coursework
- Checking factored-form answers
- Graphing parabola x-intercepts
- Physics and engineering modeling with second-degree equations
Final note
If your equation can be factored easily, factoring may be faster. But the quadratic formula always works for valid quadratic equations, which makes it the most reliable method for finding roots.