TetraKitsQuadratic Calculator
Solve any quadratic equation ax² + bx + c = 0 in seconds. Enter the three coefficients and read both roots, the discriminant (Δ), and whether solutions are real or complex — powered by the quadratic formula.
Read: Quadratic Equation Guide: Formula, Discriminant & Roots →
- Free to Use
- No Signup
- Privacy Friendly
How to solve a quadratic equation
- 1
Enter coefficients
Type values for a, b, and c in ax² + bx + c = 0. Example: x² − 5x + 6 = 0 → a=1, b=−5, c=6.
- 2
Read the discriminant
Δ = b² − 4ac determines the nature of roots: positive = two real, zero = one repeated, negative = complex conjugates.
- 3
Check both roots
See x₁ and x₂ calculated via the quadratic formula. For other math, try fractions or the scientific calculator.
Quadratic formula
- Δ > 0 — two distinct real roots
- Δ = 0 — one repeated real root
- Δ < 0 — two complex conjugate roots
Example: x² − 5x + 6 = 0 → x = 2 or x = 3.
Why Use This Tool?
Full Solutions
Real roots, complex roots, and discriminant in one view.
Step-Ready Output
See both roots and Δ to verify homework by hand.
Quick Input
Three coefficient fields with instant results.
Local Math
Equations never leave your browser.
Frequently Asked Questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / 2a. It finds the roots of any quadratic equation where a ≠ 0.
What does a negative discriminant mean?
When Δ = b² − 4ac < 0, there are no real roots — only complex conjugate solutions involving imaginary numbers.
What if a equals zero?
When a = 0, the equation is linear (bx + c = 0), not quadratic. The calculator solves for x = −c/b instead.
Can I enter decimal coefficients?
Yes. Any real numbers work — integers, decimals, and negatives.
Is this quadratic calculator free?
Yes. Free with unlimited equations and no signup.
Quadratic Roots Without Manual Formula Work
Algebra homework, engineering problems, and physics equations all reduce to ax² + bx + c = 0. This calculator applies the quadratic formula instantly, showing discriminant, both roots, and complex results when needed.
