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} - 4 x + 3 = (- 2)^{2} - 4 * (- 2) + 3 x^{2} - 4 x - 12 = 0 a = 1; b = - 4; c = - 12 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot (- 12) = 64 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 6 4}{2} x_{1, 2} = \frac{4 \pm 8}{2} x_{1, 2} = 2 \pm 4 x_{1} = 6 x_{2} = - 2 Factored form of the equation: (x - 6) (x + 2) = 0

Solution in text:

x²-4x-12=0 ... quadratic equation

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

x₁ = 6
x₂ = -2

P = {6; -2}