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:

48 = 4 * 6 * a + 2 * a^{2} - 2 a^{2} - 24 a + 48 = 0 2 a^{2} + 24 a - 48 = 0 2 . . . prime number 24 = 2^{3} \cdot 3 48 = 2^{4} \cdot 3 GCD (2, 24, 48) = 2 = 2 a^{2} + 12 a - 24 = 0 p = 1; q = 12; r = - 24 D = q^{2} - 4 p r = 1 2^{2} - 4 \cdot 1 \cdot (- 24) = 240 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 1 2 \pm 2 4 0}{2} = \frac{- 1 2 \pm 4 1 5}{2} a_{1, 2} = - 6 \pm 7.745967 a_{1} = 1.745966692 a_{2} = - 13.745966692 Factored form of the equation: (a - 1.745966692) (a + 13.745966692) = 0

Solution in text:

-2a²-24a+48=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 960
D > 0 ... The equation has two distinct real roots

a₁ = 1.7459667
a₂ = -13.7459667

P = {1.7459667; -13.7459667}