Ax² + bx +c = 0
rewrite as x² + b/a x + c/a = 0 call - b/a = b' c/a = c'
x² - b' x + c' = 0 equaiton 1
IF α and β are the roots,
(x - α) (x - β) = 0 expand this expression then, we get
x² - (α+ β) x +αβ = 0 comparew with the equation 1
α+β = b' abd αβ = product
Convert the equation in the form of equation 1 and then try to factor the c' so that the sum of the factors becomes minus of coefficient of x.
If some trial values fail, use the formula
Δ = √b² - 4ac and α, β = (-b +- Δ)/2
Often trying simple values of x as x=1, -1, -2, -3, 2, 3 could give a root directly.