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:

360 (x - 3) + 360 x = 117 * x * (x - 3) - 117 x^{2} + 1071 x - 1080 = 0 117 x^{2} - 1071 x + 1080 = 0 117 = 3^{2} \cdot 13 1071 = 3^{2} \cdot 7 \cdot 17 1080 = 2^{3} \cdot 3^{3} \cdot 5 GCD (117, 1071, 1080) = 3^{2} = 9 13 x^{2} - 119 x + 120 = 0 a = 13; b = - 119; c = 120 D = b^{2} - 4 a c = 11 9^{2} - 4 \cdot 13 \cdot 120 = 7921 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 1 9 \pm 7 9 2 1}{2 6} x_{1, 2} = \frac{1 1 9 \pm 8 9}{2 6} x_{1, 2} = 4.576923 \pm 3.423077 x_{1} = 8 x_{2} = 1.153846154 Factored form of the equation: 13 (x - 8) (x - 1.153846154) = 0

Solution in text:

-117x²+1071x-1080=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 641601
D > 0 ... The equation has two distinct real roots

x₁ = 8
x₂ = 1.1538462

P = {8; 1.1538462}