Quadratic Solver
ax² + bx + c = 0
Solution
Enter coefficients and click Calculate
Quadratic Equations
The Quadratic Formula
The quadratic formula provides the solution(s) to a quadratic equation of the form:
ax² + bx + c = 0
Where a, b, and c are coefficients, and a ≠ 0.
The Formula
The solutions are given by:
x = [-b ± √(b² - 4ac)] / (2a)
Discriminant
The expression inside the square root (b² - 4ac) is called the discriminant (D).
- D > 0: Two distinct real roots
- D = 0: One real root (repeated)
- D < 0: Two complex roots
Example Calculation
For the equation: 2x² + 5x - 3 = 0
Where a = 2, b = 5, c = -3
Discriminant D = b² - 4ac = 25 - 4(2)(-3) = 25 + 24 = 49
Solutions:
x = [-5 ± √49]/(4) = [-5 ± 7]/4
So x₁ = (-5 + 7)/4 = 0.5
x₂ = (-5 - 7)/4 = -3