(8x-16)(6x+20)=180

Solution for (8x-16)(6x+20)=180 equation:

(8x-16)(6x+20)=180

We move all terms to the left:

(8x-16)(6x+20)-(180)=0

We multiply parentheses ..

(+48x^2+160x-96x-320)-180=0

We get rid of parentheses

48x^2+160x-96x-320-180=0

We add all the numbers together, and all the variables

48x^2+64x-500=0

a = 48; b = 64; c = -500;
Δ = b2-4ac
Δ = 642-4·48·(-500)
Δ = 100096
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:

$\sqrt{\Delta}=\sqrt{100096}=\sqrt{256*391}=\sqrt{256}*\sqrt{391}=16\sqrt{391}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-16\sqrt{391}}{2*48}=\frac{-64-16\sqrt{391}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+16\sqrt{391}}{2*48}=\frac{-64+16\sqrt{391}}{96}
$