(X+12)(y+6)=169

Solution for (X+12)(y+6)=169 equation:

(X+12)(X+6)=169

We move all terms to the left:

(X+12)(X+6)-(169)=0

We multiply parentheses ..

(+X^2+6X+12X+72)-169=0

We get rid of parentheses

X^2+6X+12X+72-169=0

We add all the numbers together, and all the variables

X^2+18X-97=0

a = 1; b = 18; c = -97;
Δ = b2-4ac
Δ = 182-4·1·(-97)
Δ = 712
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:

$\sqrt{\Delta}=\sqrt{712}=\sqrt{4*178}=\sqrt{4}*\sqrt{178}=2\sqrt{178}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{178}}{2*1}=\frac{-18-2\sqrt{178}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{178}}{2*1}=\frac{-18+2\sqrt{178}}{2}
$