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:

(2 a - 72) a = - 72 * (5 - a) 2 a^{2} - 144 a + 360 = 0 2 . . . prime number 144 = 2^{4} \cdot 3^{2} 360 = 2^{3} \cdot 3^{2} \cdot 5 GCD (2, 144, 360) = 2 = 2 a^{2} - 72 a + 180 = 0 p = 1; q = - 72; r = 180 D = q^{2} - 4 p r = 7 2^{2} - 4 \cdot 1 \cdot 180 = 4464 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{7 2 \pm 4 4 6 4}{2} = \frac{7 2 \pm 1 2 3 1}{2} a_{1, 2} = 36 \pm 33.406586 a_{1} = 69.406586177 a_{2} = 2.593413823 Factored form of the equation: (a - 69.406586177) (a - 2.593413823) = 0

Solution in text:

2a²-144a+360=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 17856
D > 0 ... The equation has two distinct real roots

a₁ = 69.4065862
a₂ = 2.5934138

P = {69.4065862; 2.5934138}