What is it?
The Quadratic Equation Solver solves equations of the form ax² + bx + c = 0. It shows the roots, the discriminant (b² − 4ac), what kind of roots they are, and the vertex of the curve.
Who is it for?
Class 9–12 students, teachers checking answers, and anyone solving second-degree equations.
How to use it
Enter a, b and c. Bring the equation to the form ax² + bx + c = 0 first: x² = 5x − 6 becomes x² − 5x + 6 = 0, so a = 1, b = −5, c = 6. The answer appears as you type; there is no Calculate button. Tap Copy result to copy it, or Share on WhatsApp to send it.
What the discriminant tells you
- Positive: two different real roots (the graph crosses the x-axis twice).
- Zero: one repeated root (the graph touches the axis).
- Negative: no real roots; two complex roots like 2 ± 3i.
The vertex
The highest or lowest point of the parabola, at x = −b ÷ 2a. If a is positive, it is the lowest point (minimum).
Common mistakes
- Forgetting the sign: for x² − 5x + 6, b is −5, not 5.
- a can’t be 0: then it isn’t quadratic. Solve bx + c = 0 instead.
- A missing term means 0: for x² − 9 = 0, b = 0.
Formula: x = (−b ± √(b² − 4ac)) ÷ 2a.
Errors and how to fix them
- “a cannot be 0 (then it is not quadratic)”: solve bx + c = 0 instead.
Open the tool: Quadratic Equation Solver
Still stuck?
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Questions, or an error not listed here?
Tell us in the comments: what you were doing, the exact message you saw, and your device and browser. We read every comment and add new fixes to this article.