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:

6 * (x - 10) + 6 * x = (x - 10) * x - x^{2} + 22 x - 60 = 0 x^{2} - 22 x + 60 = 0 a = 1; b = - 22; c = 60 D = b^{2} - 4 a c = 2 2^{2} - 4 \cdot 1 \cdot 60 = 244 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 2 \pm 2 4 4}{2} = \frac{2 2 \pm 2 6 1}{2} x_{1, 2} = 11 \pm 7.81025 x_{1} = 18.810249676 x_{2} = 3.189750324 Factored form of the equation: (x - 18.810249676) (x - 3.189750324) = 0

Solution in text:

-x²+22x-60=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 244
D > 0 ... The equation has two distinct real roots

x₁ = 18.8102497
x₂ = 3.1897503

P = {18.8102497; 3.1897503}