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:

(70312 + 2 * w) * (w - 1) = 70312 * w 2 w^{2} - 2 w - 70312 = 0 2 . . . prime number 70312 = 2^{3} \cdot 11 \cdot 17 \cdot 47 GCD (2, 2, 70312) = 2 = 2 w^{2} - w - 35156 = 0 a = 1; b = - 1; c = - 35156 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 1 \cdot (- 35156) = 140625 D > 0 w_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 \pm 1 4 0 6 2 5}{2} w_{1, 2} = \frac{1 \pm 3 7 5}{2} w_{1, 2} = 0.5 \pm 187.5 w_{1} = 188 w_{2} = - 187 Factored form of the equation: (w - 188) (w + 187) = 0

Solution in text:

2w²-2w-70312=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 562500
D > 0 ... The equation has two distinct real roots

w₁ = 188
w₂ = -187

P = {188; -187}