Quadratic equation calculator

Quadratic equation has the basic form:

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

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

x^{2} + 3 x + 2.25 = 0 x^{2} + 3 x + 2.25 = 0 a = 1; b = 3; c = 2.25 D = b^{2} - 4 a c = 3^{2} - 4 \cdot 1 \cdot 2.25 = 0 D = 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 \pm 0}{2} x_{1, 2} = \frac{- 3 \pm 0}{2} x_{1, 2} = - 1.5 \pm 0 x_{1} = x_{2} = - 1.5 Factored form of the equation: (x + 1.5) (x + 1.5) = 0

Solution in text:

x²+3x+2.25=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}