(x-17)(x-22)=0

Solution for (x-17)(x-22)=0 equation:

(x-17)(x-22)=0

We multiply parentheses ..

(+x^2-22x-17x+374)=0

We get rid of parentheses

x^2-22x-17x+374=0

We add all the numbers together, and all the variables

x^2-39x+374=0

a = 1; b = -39; c = +374;
Δ = b2-4ac
Δ = -392-4·1·374
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-5}{2*1}=\frac{34}{2}
=17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+5}{2*1}=\frac{44}{2}
=22
$