Quadratic equation calculator

Quadratic equation has the basic form:

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

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

(388128 + 4 * w) * (w - 1) = 388128 * w 4 w^{2} - 4 w - 388128 = 0 4 = 2^{2} 388128 = 2^{5} \cdot 3 \cdot 13 \cdot 311 GCD (4, 4, 388128) = 2^{2} = 4 w^{2} - w - 97032 = 0 a = 1; b = - 1; c = - 97032 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 1 \cdot (- 97032) = 388129 D > 0 w_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 \pm 3 8 8 1 2 9}{2} w_{1, 2} = \frac{1 \pm 6 2 3}{2} w_{1, 2} = 0.5 \pm 311.5 w_{1} = 312 w_{2} = - 311 Factored form of the equation: (w - 312) (w + 311) = 0

Solution in text:

4w²-4w-388128=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 6210064
D > 0 ... The equation has two distinct real roots

w₁ = 312
w₂ = -311

P = {312; -311}