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 - 8 * ((m^{2} + 4) / 4) + 20 = 0 - m^{2} + 4 m + 12 = 0 m^{2} - 4 m - 12 = 0 a = 1; b = - 4; c = - 12 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot (- 12) = 64 D > 0 m_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 6 4}{2} m_{1, 2} = \frac{4 \pm 8}{2} m_{1, 2} = 2 \pm 4 m_{1} = 6 m_{2} = - 2 Factored form of the equation: (m - 6) (m + 2) = 0

Solution in text:

-m²+4m+12=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 64
D > 0 ... The equation has two distinct real roots

m₁ = 6
m₂ = -2

P = {6; -2}