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 - 6) + x = 1 / 20 * (x - 6) * x - 0.05 x^{2} + 2.3 x - 6 = 0 0.05 x^{2} - 2.3 x + 6 = 0 a = 0.05; b = - 2.3; c = 6 D = b^{2} - 4 a c = 2 . 3^{2} - 4 \cdot 0.05 \cdot 6 = 4.09 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 . 3 \pm 4 . 0 9}{0 . 1} = 23 \pm 409 x_{1, 2} = 23 \pm 20.223748 x_{1} = 43.223748416 x_{2} = 2.776251584 Factored form of the equation: 0.05 (x - 43.223748416) (x - 2.776251584) = 0

Solution in text:

-0.05x²+2.3x-6=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 4.09
D > 0 ... The equation has two distinct real roots

x₁ = 43.2237484
x₂ = 2.7762516

P = {43.2237484; 2.7762516}