posted by omar .
Find the roots of the given equation by completing the square.
αx^2 + βx + δ = 0
Do you mean ax^2+ bx+c=0 ??
I think that's safe. The symbols used don't really matter. It's easier to type Roman letters, so I'll use those
ax^2 + bx + c = 0
a(x^2 + b/a x) = -c
a(x^2 + b/a x + (b/2a)^2) = (b/2a)^2 - c
a(x + (b/2a))^2 = (b^2 - 4ac)/4a
(x + b/2a)^2 = (b^2 - 4ac)/4a^2
x + b/2a = ±√(b^2 - 4ac)/2a
x = [-b ± √(b^2 - 4ac)]/2a