(x+5)(x-22)=0

Solution for (x+5)(x-22)=0 equation:

(x+5)(x-22)=0

We multiply parentheses ..

(+x^2-22x+5x-110)=0

We get rid of parentheses

x^2-22x+5x-110=0

We add all the numbers together, and all the variables

x^2-17x-110=0

a = 1; b = -17; c = -110;
Δ = b2-4ac
Δ = -172-4·1·(-110)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-27}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+27}{2*1}=\frac{44}{2}
=22
$