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:

600 * x = 600 * (x - 200) + 0.5 * (x - 200) * x - 0.5 x^{2} + 100 x + 120000 = 0 0.5 x^{2} - 100 x - 120000 = 0 a = 0.5; b = - 100; c = - 120000 D = b^{2} - 4 a c = 10 0^{2} - 4 \cdot 0.5 \cdot (- 120000) = 250000 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 0 0 \pm 2 5 0 0 0 0}{1} = 100 \pm 5001 x_{1, 2} = 100 \pm 500 x_{1} = 600 x_{2} = - 400 Factored form of the equation: 0.5 (x - 600) (x + 400) = 0

Solution in text:

-0.5x²+100x+120000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 250000
D > 0 ... The equation has two distinct real roots

x₁ = 600
x₂ = -400

P = {600; -400}