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:

(90 - x) * 90 * 60 + x * (90 - x) * 27 = 60 * 90 * x - 27 x^{2} - 8370 x + 486000 = 0 27 x^{2} + 8370 x - 486000 = 0 27 = 3^{3} 8370 = 2 \cdot 3^{3} \cdot 5 \cdot 31 486000 = 2^{4} \cdot 3^{5} \cdot 5^{3} GCD (27, 8370, 486000) = 3^{3} = 27 x^{2} + 310 x - 18000 = 0 a = 1; b = 310; c = - 18000 D = b^{2} - 4 a c = 31 0^{2} - 4 \cdot 1 \cdot (- 18000) = 168100 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 1 0 \pm 1 6 8 1 0 0}{2} x_{1, 2} = \frac{- 3 1 0 \pm 4 1 0}{2} x_{1, 2} = - 155 \pm 205 x_{1} = 50 x_{2} = - 360 Factored form of the equation: (x - 50) (x + 360) = 0

Solution in text:

-27x²-8370x+486000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 122544900
D > 0 ... The equation has two distinct real roots

x₁ = 50
x₂ = -360

P = {50; -360}