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:

75 = 3 n^{2} + 3 n + 1 - 16 - 3 n^{2} - 3 n + 90 = 0 3 n^{2} + 3 n - 90 = 0 3 . . . prime number 90 = 2 \cdot 3^{2} \cdot 5 GCD (3, 3, 90) = 3 = 3 n^{2} + n - 30 = 0 a = 1; b = 1; c = - 30 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 1 \cdot (- 30) = 121 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 \pm 1 2 1}{2} n_{1, 2} = \frac{- 1 \pm 1 1}{2} n_{1, 2} = - 0.5 \pm 5.5 n_{1} = 5 n_{2} = - 6 Factored form of the equation: (n - 5) (n + 6) = 0

Solution in text:

-3n²-3n+90=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1089
D > 0 ... The equation has two distinct real roots

n₁ = 5
n₂ = -6

P = {5; -6}