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:

n * (n - 1) = 2 * 2346 n^{2} - n - 4692 = 0 a = 1; b = - 1; c = - 4692 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 1 \cdot (- 4692) = 18769 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 \pm 1 8 7 6 9}{2} n_{1, 2} = \frac{1 \pm 1 3 7}{2} n_{1, 2} = 0.5 \pm 68.5 n_{1} = 69 n_{2} = - 68 Factored form of the equation: (n - 69) (n + 68) = 0

Solution in text:

n²-n-4692=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 18769
D > 0 ... The equation has two distinct real roots

n₁ = 69
n₂ = -68

P = {69; -68}