Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

4 x^{2} + 12 x + 9 = 0 a = 4; b = 12; c = 9 D = b^{2} - 4 a c = 1 2^{2} - 4 \cdot 4 \cdot 9 = 0 D = 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 2 \pm 0}{8} x_{1, 2} = \frac{- 1 2 \pm 0}{8} x_{1, 2} = - 1.5 \pm 0 x_{1} = x_{2} = - 1.5 Factored form of the equation: 4 (x + 1.5) (x + 1.5) = 0

Solution in text:

4x²+12x+9=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 0
D=0 ... The equation has one double real root

x₁ = -1.5
x₂ = -1.5

P = {-1.5}