(8r-8)(7r+6)=180

Solution for (8r-8)(7r+6)=180 equation:

(8r-8)(7r+6)=180

We move all terms to the left:

(8r-8)(7r+6)-(180)=0

We multiply parentheses ..

(+56r^2+48r-56r-48)-180=0

We get rid of parentheses

56r^2+48r-56r-48-180=0

We add all the numbers together, and all the variables

56r^2-8r-228=0

a = 56; b = -8; c = -228;
Δ = b2-4ac
Δ = -82-4·56·(-228)
Δ = 51136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{51136}=\sqrt{64*799}=\sqrt{64}*\sqrt{799}=8\sqrt{799}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{799}}{2*56}=\frac{8-8\sqrt{799}}{112}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{799}}{2*56}=\frac{8+8\sqrt{799}}{112}
$