(4x+36)(96-x)=180

Solution for (4x+36)(96-x)=180 equation:

(4x+36)(96-x)=180

We move all terms to the left:

(4x+36)(96-x)-(180)=0

We add all the numbers together, and all the variables

(4x+36)(-1x+96)-180=0

We multiply parentheses ..

(-4x^2+384x-36x+3456)-180=0

We get rid of parentheses

-4x^2+384x-36x+3456-180=0

We add all the numbers together, and all the variables

-4x^2+348x+3276=0

a = -4; b = 348; c = +3276;
Δ = b2-4ac
Δ = 3482-4·(-4)·3276
Δ = 173520
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:

$\sqrt{\Delta}=\sqrt{173520}=\sqrt{144*1205}=\sqrt{144}*\sqrt{1205}=12\sqrt{1205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(348)-12\sqrt{1205}}{2*-4}=\frac{-348-12\sqrt{1205}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(348)+12\sqrt{1205}}{2*-4}=\frac{-348+12\sqrt{1205}}{-8}
$