(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^2-27X+110=0

a = 1; b = -27; c = +110;
Δ = b2-4ac
Δ = -272-4·1·110
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-17}{2*1}=\frac{10}{2}
=5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+17}{2*1}=\frac{44}{2}
=22
$