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:

18 * (x - 10) + 18 * x = (x - 10) * x - x^{2} + 46 x - 180 = 0 x^{2} - 46 x + 180 = 0 a = 1; b = - 46; c = 180 D = b^{2} - 4 a c = 4 6^{2} - 4 \cdot 1 \cdot 180 = 1396 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 6 \pm 1 3 9 6}{2} = \frac{4 6 \pm 2 3 4 9}{2} x_{1, 2} = 23 \pm 18.681542 x_{1} = 41.681541692 x_{2} = 4.318458308 Factored form of the equation: (x - 41.681541692) (x - 4.318458308) = 0

Solution in text:

-x²+46x-180=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1396
D > 0 ... The equation has two distinct real roots

x₁ = 41.6815417
x₂ = 4.3184583

P = {41.6815417; 4.3184583}