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:

1000 = 2 * p i * x (x + 20) - 6.2831853071796 x^{2} - 125.664 x + 1000 = 0 6.2831853071796 x^{2} + 125.664 x - 1000 = 0 a = 6.283185; b = 125.664; c = - 1000 D = b^{2} - 4 a c = 125.66 4^{2} - 4 \cdot 6.283185 \cdot (- 1000) = 40924.108270461 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 2 5 . 6 6 \pm 4 0 9 2 4 . 1 1}{1 2 . 5 6 6 3 7 1} x_{1, 2} = - 10 \pm 16.09829 x_{1} = 6.098290067 x_{2} = - 26.098290067 Factored form of the equation: 6.2831853071796 (x - 6.098290067) (x + 26.098290067) = 0

Solution in text:

-6.2831853071796x²-125.66370614359x+1000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 40924.108270461
D > 0 ... The equation has two distinct real roots

x₁ = 6.0982901
x₂ = -26.0982901

P = {6.0982901; -26.0982901}