(x-30)(x+22)=0

Solution for (x-30)(x+22)=0 equation:

(x-30)(x+22)=0

We multiply parentheses ..

(+x^2+22x-30x-660)=0

We get rid of parentheses

x^2+22x-30x-660=0

We add all the numbers together, and all the variables

x^2-8x-660=0

a = 1; b = -8; c = -660;
Δ = b2-4ac
Δ = -82-4·1·(-660)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-52}{2*1}=\frac{-44}{2}
=-22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+52}{2*1}=\frac{60}{2}
=30
$