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:

12 * (x - 8) + 12 * x = (x - 8) * x - x^{2} + 32 x - 96 = 0 x^{2} - 32 x + 96 = 0 a = 1; b = - 32; c = 96 D = b^{2} - 4 a c = 3 2^{2} - 4 \cdot 1 \cdot 96 = 640 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{3 2 \pm 6 4 0}{2} = \frac{3 2 \pm 8 1 0}{2} x_{1, 2} = 16 \pm 12.649111 x_{1} = 28.649110641 x_{2} = 3.350889359 Factored form of the equation: (x - 28.649110641) (x - 3.350889359) = 0

Solution in text:

-x²+32x-96=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 640
D > 0 ... The equation has two distinct real roots

x₁ = 28.6491106
x₂ = 3.3508894

P = {28.6491106; 3.3508894}