Calculating the root of a quadratic equation

Starting with:

ax² + bx + c = 0

the two possible roots are given by

x₁ = (-b + (b² - 4ac)^0.5) / 2a

x₂ = (-b - (b² - 4ac)^0.5) / 2a

Depending on the domain in which the solution can lie, you might have to check the discriminant for being smaller than 0. The discriminant is the part inside the square root: b² - 4ac.
If the domain of the solution are the real numbers R then the discriminant being less than zero will mean that there is no solution. Should the domain be in the set of complex numbers C a solution will exist even if the discriminant is less than zero:

x₁ = -b/2a + J(|b² - 4ac|)^0.5/2a
x₂ = -b/2a - J(|b² - 4ac|)^0.5/2a

Solutions of quadratic equations are always complex conjugates of each other when the discriminant is smaller than zero.

Should the discriminant be zero x₁ = x₂ = -b / 2a there is only one solution.

Now all that is left to do is input the coefficients a,b,c and do the calculations.
I don't think you'll find that too hard to do. Just give it a try!

Regards,

— Manfred

If you know how to solve it manually (you know that, right?) then you have the algorithm.

see below link.
Link 1[^]