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:

8 * x = (x + 2) * (6 x - 8) - 6 x^{2} + 4 x + 16 = 0 6 x^{2} - 4 x - 16 = 0 6 = 2 \cdot 3 4 = 2^{2} 16 = 2^{4} GCD (6, 4, 16) = 2 = 2 3 x^{2} - 2 x - 8 = 0 a = 3; b = - 2; c = - 8 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 3 \cdot (- 8) = 100 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 \pm 1 0 0}{6} x_{1, 2} = \frac{2 \pm 1 0}{6} x_{1, 2} = 0.333333 \pm 1.666667 x_{1} = 2 x_{2} = - 1.333333333 Factored form of the equation: 3 (x - 2) (x + 1.333333333) = 0

Solution in text:

-6x²+4x+16=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 400
D > 0 ... The equation has two distinct real roots

x₁ = 2
x₂ = -1.3333333

P = {2; -1.3333333}