(8x+16)(6x-60)=180

Solution for (8x+16)(6x-60)=180 equation:

(8x+16)(6x-60)=180

We move all terms to the left:

(8x+16)(6x-60)-(180)=0

We multiply parentheses ..

(+48x^2-480x+96x-960)-180=0

We get rid of parentheses

48x^2-480x+96x-960-180=0

We add all the numbers together, and all the variables

48x^2-384x-1140=0

a = 48; b = -384; c = -1140;
Δ = b2-4ac
Δ = -3842-4·48·(-1140)
Δ = 366336
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:

$\sqrt{\Delta}=\sqrt{366336}=\sqrt{2304*159}=\sqrt{2304}*\sqrt{159}=48\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-48\sqrt{159}}{2*48}=\frac{384-48\sqrt{159}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+48\sqrt{159}}{2*48}=\frac{384+48\sqrt{159}}{96}
$