Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

(20 + x) * (30 + x) = 2 * 20 * 30 x^{2} + 50 x - 600 = 0 a = 1; b = 50; c = - 600 D = b^{2} - 4 a c = 5 0^{2} - 4 \cdot 1 \cdot (- 600) = 4900 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 5 0 \pm 4 9 0 0}{2} x_{1, 2} = \frac{- 5 0 \pm 7 0}{2} x_{1, 2} = - 25 \pm 35 x_{1} = 10 x_{2} = - 60 Factored form of the equation: (x - 10) (x + 60) = 0

Solution in text:

x²+50x-600=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 4900
D > 0 ... The equation has two distinct real roots

x₁ = 10
x₂ = -60

P = {10; -60}