(7x+2)(8x-8)=180

Solution for (7x+2)(8x-8)=180 equation:

(7x+2)(8x-8)=180

We move all terms to the left:

(7x+2)(8x-8)-(180)=0

We multiply parentheses ..

(+56x^2-56x+16x-16)-180=0

We get rid of parentheses

56x^2-56x+16x-16-180=0

We add all the numbers together, and all the variables

56x^2-40x-196=0

a = 56; b = -40; c = -196;
Δ = b2-4ac
Δ = -402-4·56·(-196)
Δ = 45504
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:

$\sqrt{\Delta}=\sqrt{45504}=\sqrt{576*79}=\sqrt{576}*\sqrt{79}=24\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-24\sqrt{79}}{2*56}=\frac{40-24\sqrt{79}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+24\sqrt{79}}{2*56}=\frac{40+24\sqrt{79}}{112}
$