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:

m 2 = 4 m + 20 m^{2} - 4 m - 20 = 0 a = 1; b = - 4; c = - 20 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot (- 20) = 96 D > 0 m_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 9 6}{2} = \frac{4 \pm 4 6}{2} m_{1, 2} = 2 \pm 4.898979 m_{1} = 6.898979486 m_{2} = - 2.898979486 Factored form of the equation: (m - 6.898979486) (m + 2.898979486) = 0

Solution in text:

m²-4m-20=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 96
D > 0 ... The equation has two distinct real roots

m₁ = 6.8989795
m₂ = -2.8989795

P = {6.8989795; -2.8989795}