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 A * 3 * (A + 1) = 810 9 A^{2} + 9 A - 810 = 0 9 = 3^{2} 810 = 2 \cdot 3^{4} \cdot 5 GCD (9, 9, 810) = 3^{2} = 9 A^{2} + A - 90 = 0 a = 1; b = 1; c = - 90 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 1 \cdot (- 90) = 361 D > 0 A_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 \pm 3 6 1}{2} A_{1, 2} = \frac{- 1 \pm 1 9}{2} A_{1, 2} = - 0.5 \pm 9.5 A_{1} = 9 A_{2} = - 10 Factored form of the equation: (A - 9) (A + 10) = 0

Solution in text:

9A²+9A-810=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 29241
D > 0 ... The equation has two distinct real roots

A₁ = 9
A₂ = -10

P = {9; -10}