Implementation of the Po-Shen Loh method of calculating Quadratics, without usign the quadratic formula (inspired by https://www.poshenloh.com/quadraticdetail/)
In a quadratic equation: f(x) = ax^2 + bx + c = 0
also,
f(x) = (x-m)(x-n) = 0 In the above statement, m + n = b and m * n = c
Now this is where you'll see change in the flow,
m * n = c and, m + n = b
Now for every two numbers whose sum is b, their average is b/2 (e.g., 7, 4 => 7+4 = 11 => (7+4)/2 = 11/2 = b/2)
So,
m = u-a
n = u+a
where a is the average (b/2)
m * n = c (u-a)(u+a) = c u^2 - a^2 = c u = sqrt(a^2 - c)
u-a, u+a are the roots of the equation.