(x-22)(x-16)=9

Solution for (x-22)(x-16)=9 equation:

(x-22)(x-16)=9

We move all terms to the left:

(x-22)(x-16)-(9)=0

We multiply parentheses ..

(+x^2-16x-22x+352)-9=0

We get rid of parentheses

x^2-16x-22x+352-9=0

We add all the numbers together, and all the variables

x^2-38x+343=0

a = 1; b = -38; c = +343;
Δ = b2-4ac
Δ = -382-4·1·343
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-6\sqrt{2}}{2*1}=\frac{38-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+6\sqrt{2}}{2*1}=\frac{38+6\sqrt{2}}{2}
$