(x+96)(x+78)=180

Solution for (x+96)(x+78)=180 equation:

(x+96)(x+78)=180

We move all terms to the left:

(x+96)(x+78)-(180)=0

We multiply parentheses ..

(+x^2+78x+96x+7488)-180=0

We get rid of parentheses

x^2+78x+96x+7488-180=0

We add all the numbers together, and all the variables

x^2+174x+7308=0

a = 1; b = 174; c = +7308;
Δ = b2-4ac
Δ = 1742-4·1·7308
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(174)-6\sqrt{29}}{2*1}=\frac{-174-6\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(174)+6\sqrt{29}}{2*1}=\frac{-174+6\sqrt{29}}{2}
$