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:

119380.52083641 = p i / 3 * 60 * (x^{2} + x * (10 + x) + (10 + x)^{2}) - 188.49555921539 x^{2} - 1884.956 x + 113097.336 = 0 188.49555921539 x^{2} + 1884.956 x - 113097.336 = 0 a = 188.495559; b = 1884.956; c = - 113097.336 D = b^{2} - 4 a c = 1884.95 6^{2} - 4 \cdot 188.495559 \cdot (- 113097.336) = 88826439.609802 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 8 8 4 . 9 6 \pm 8 8 8 2 6 4 3 9 . 6 1}{3 7 6 . 9 9 1 1 1 8} x_{1, 2} = - 5 \pm 25 x_{1} = 20 x_{2} = - 30 Factored form of the equation: 188.49555921539 (x - 20) (x + 30) = 0

Solution in text:

-188.49555921539x²-1884.9555921539x+113097.33552923=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 88826439.609802
D > 0 ... The equation has two distinct real roots

x₁ = 20
x₂ = -30

P = {20; -30}