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:

- 3 x^{2} - 2 * 33 * x + 33 * 33 = 0 - 3 x^{2} - 66 x + 1089 = 0 3 x^{2} + 66 x - 1089 = 0 3 . . . prime number 66 = 2 \cdot 3 \cdot 11 1089 = 3^{2} \cdot 1 1^{2} GCD (3, 66, 1089) = 3 = 3 x^{2} + 22 x - 363 = 0 a = 1; b = 22; c = - 363 D = b^{2} - 4 a c = 2 2^{2} - 4 \cdot 1 \cdot (- 363) = 1936 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 2 \pm 1 9 3 6}{2} x_{1, 2} = \frac{- 2 2 \pm 4 4}{2} x_{1, 2} = - 11 \pm 22 x_{1} = 11 x_{2} = - 33 Factored form of the equation: (x - 11) (x + 33) = 0

Solution in text:

-3x²-66x+1089=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 17424
D > 0 ... The equation has two distinct real roots

x₁ = 11
x₂ = -33

P = {11; -33}