Quadratic Equation Solver
Enter a, b, and c to find the roots using the quadratic formula, including complex roots.
Calculator
Use the Quadratic Equation Solver
Result
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Formula
x = (−b ± √(b² − 4ac)) ÷ 2a
Step-by-step
- 1
Enter coefficients
Provide a (≠ 0), b, and c.
- 2
Compute discriminant
D = b² − 4ac determines the root type.
- 3
Read the roots
Two real, one repeated, or complex roots.
Worked example
Example input: a: 1, b: -3, c: 2
Result: roots: 2, 1
Related tools
- Linear Equation Solver
Solve a·x + b = c.
Frequently asked questions
What does the discriminant tell me?
D > 0: two real roots. D = 0: one repeated root. D < 0: two complex conjugate roots.
How are complex roots displayed here?
When the discriminant falls below zero the answer prints in a plus-minus bi form: a real center value with an imaginary branch, written with the i notation. The list of real roots stays empty because none exist on the real number line.
What does the example 1, -3, 2 return?
Roots 2 and 1 — substituting back, 1 x 4 minus 3 x 2 plus 2 equals 0 and 1 x 1 minus 3 x 1 plus 2 equals 0. The discriminant of that pair is 1, which is why two real roots appear rather than any other form.