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:

3 n^{2} - 213 n + 3312 = 0 3 n^{2} - 213 n + 3312 = 0 3 . . . prime number 213 = 3 \cdot 71 3312 = 2^{4} \cdot 3^{2} \cdot 23 GCD (3, 213, 3312) = 3 = 3 n^{2} - 71 n + 1104 = 0 a = 1; b = - 71; c = 1104 D = b^{2} - 4 a c = 7 1^{2} - 4 \cdot 1 \cdot 1104 = 625 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{7 1 \pm 6 2 5}{2} n_{1, 2} = \frac{7 1 \pm 2 5}{2} n_{1, 2} = 35.5 \pm 12.5 n_{1} = 48 n_{2} = 23 Factored form of the equation: (n - 48) (n - 23) = 0

Solution in text:

3n²-213n+3312=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 5625
D > 0 ... The equation has two distinct real roots

n₁ = 48
n₂ = 23

P = {48; 23}