(x+75)(x+117)=180

Solution for (x+75)(x+117)=180 equation:

(x+75)(x+117)=180

We move all terms to the left:

(x+75)(x+117)-(180)=0

We multiply parentheses ..

(+x^2+117x+75x+8775)-180=0

We get rid of parentheses

x^2+117x+75x+8775-180=0

We add all the numbers together, and all the variables

x^2+192x+8595=0

a = 1; b = 192; c = +8595;
Δ = b2-4ac
Δ = 1922-4·1·8595
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-6\sqrt{69}}{2*1}=\frac{-192-6\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+6\sqrt{69}}{2*1}=\frac{-192+6\sqrt{69}}{2}
$