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 - 6) + 18 * x = (x - 6) * x - x^{2} + 42 x - 108 = 0 x^{2} - 42 x + 108 = 0 a = 1; b = - 42; c = 108 D = b^{2} - 4 a c = 4 2^{2} - 4 \cdot 1 \cdot 108 = 1332 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 2 \pm 1 3 3 2}{2} = \frac{4 2 \pm 6 3 7}{2} x_{1, 2} = 21 \pm 18.248288 x_{1} = 39.248287591 x_{2} = 2.751712409 Factored form of the equation: (x - 39.248287591) (x - 2.751712409) = 0

Solution in text:

-x²+42x-108=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1332
D > 0 ... The equation has two distinct real roots

x₁ = 39.2482876
x₂ = 2.7517124

P = {39.2482876; 2.7517124}