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Quadratic Equation Solver

MATH

Solve quadratic equations ax²+bx+c=0 with real solutions.

📖 How to Use Quadratic Equation Solver

1
Enter coefficients a, b, and c
For the equation ax²+bx+c=0, enter each coefficient.
2
View solutions
The solver shows real roots using the quadratic formula, or indicates complex roots if the discriminant is negative.

💡 Examples

Two real roots
INPUT
a=1, b=-5, c=6
OUTPUT
x = 3 or x = 2 (roots of x²-5x+6=0)
Difference of squares
INPUT
a=1, b=0, c=-9
OUTPUT
x = 3 or x = -3 (roots of x²-9=0)
Complex roots
INPUT
a=1, b=0, c=1
OUTPUT
No real roots (complex: x = ±i)

🚀 Pro Tips

The discriminant (b²-4ac) tells you the nature of roots: >0 two real roots, =0 one repeated root, <0 complex roots.
Always check your answer by substituting back: if x=3, does 1(3)²-5(3)+6 = 0?
Factoring is faster when roots are integers — use the quadratic formula when factoring is hard.

Frequently Asked Questions

What is the quadratic formula?+
x = (-b ± √(b²-4ac)) / 2a. It finds the two solutions for any quadratic equation ax²+bx+c=0.
What does it mean when there are no real roots?+
The parabola does not cross the x-axis. The roots are complex numbers (involving the imaginary unit i = √-1). This is valid in higher mathematics but has no real-number solution.

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