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

Solution for (X+12)(y+6)=169X-y+6=0 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(X+12)(X+6)-(168X+6)=0

We get rid of parentheses

(X+12)(X+6)-168X-6=0

We multiply parentheses ..

(+X^2+6X+12X+72)-168X-6=0

We get rid of parentheses

X^2+6X+12X-168X+72-6=0

We add all the numbers together, and all the variables

X^2-150X+66=0

a = 1; b = -150; c = +66;
Δ = b2-4ac
Δ = -1502-4·1·66
Δ = 22236
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:

$\sqrt{\Delta}=\sqrt{22236}=\sqrt{4*5559}=\sqrt{4}*\sqrt{5559}=2\sqrt{5559}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5559}}{2*1}=\frac{150-2\sqrt{5559}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5559}}{2*1}=\frac{150+2\sqrt{5559}}{2}
$