(3x+2)(8x-8)=180

Solution for (3x+2)(8x-8)=180 equation:

(3x+2)(8x-8)=180

We move all terms to the left:

(3x+2)(8x-8)-(180)=0

We multiply parentheses ..

(+24x^2-24x+16x-16)-180=0

We get rid of parentheses

24x^2-24x+16x-16-180=0

We add all the numbers together, and all the variables

24x^2-8x-196=0

a = 24; b = -8; c = -196;
Δ = b2-4ac
Δ = -82-4·24·(-196)
Δ = 18880
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:

$\sqrt{\Delta}=\sqrt{18880}=\sqrt{64*295}=\sqrt{64}*\sqrt{295}=8\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{295}}{2*24}=\frac{8-8\sqrt{295}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{295}}{2*24}=\frac{8+8\sqrt{295}}{48}
$