About quadratic equations
This solver finds the roots of any quadratic equation ax² + bx + c = 0. Enter the coefficients a, b and c and it returns the real or complex roots using the quadratic formula, along with the discriminant that tells you how many real solutions exist. It runs entirely in your browser.
How Quadratic Solver works
How to solve a quadratic
- Enter the coefficients a, b and c (a cannot be 0).
- The roots and discriminant appear instantly.
- Read whether the roots are real or complex.
The discriminant
The discriminant is b² − 4ac. If it is positive there are two real roots; if zero there is one repeated root; if negative the two roots are complex.
The quadratic formula
The roots are x = (−b ± √(b² − 4ac)) / 2a. This tool applies it precisely, including complex results when the discriminant is negative.
Common uses
- Solve quadratic equations for x
- Find real or complex roots
- Calculate the discriminant
- Check algebra homework
- Factorise or analyse parabolas
- Find where a parabola crosses the x-axis
- Study for maths exams
- Verify hand calculations
Frequently asked questions
How do I solve a quadratic equation?
Enter a, b and c — the tool applies the quadratic formula and shows the roots and discriminant.
What is the discriminant?
b² − 4ac. It tells you whether there are two real roots, one repeated root, or two complex roots.
Can it give complex roots?
Yes — when the discriminant is negative it shows the two complex roots.
Why must a not be 0?
If a is 0 the equation is linear, not quadratic.
What does a repeated root mean?
The parabola touches the x-axis at exactly one point (discriminant = 0).
Is my data uploaded?
No — it solves entirely in your browser.
Does it show the vertex?
Yes — the note shows the x-coordinate of the vertex.
Is it free?
Yes — completely free with no sign-up.