(X+2)(y-6)=105

Solution for (X+2)(y-6)=105 equation:

(X+2)(X-6)=105

We move all terms to the left:

(X+2)(X-6)-(105)=0

We multiply parentheses ..

(+X^2-6X+2X-12)-105=0

We get rid of parentheses

X^2-6X+2X-12-105=0

We add all the numbers together, and all the variables

X^2-4X-117=0

a = 1; b = -4; c = -117;
Δ = b2-4ac
Δ = -42-4·1·(-117)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-22}{2*1}=\frac{-18}{2}
=-9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+22}{2*1}=\frac{26}{2}
=13
$