(5r-5)(8r+3)=180

Solution for (5r-5)(8r+3)=180 equation:

(5r-5)(8r+3)=180

We move all terms to the left:

(5r-5)(8r+3)-(180)=0

We multiply parentheses ..

(+40r^2+15r-40r-15)-180=0

We get rid of parentheses

40r^2+15r-40r-15-180=0

We add all the numbers together, and all the variables

40r^2-25r-195=0

a = 40; b = -25; c = -195;
Δ = b2-4ac
Δ = -252-4·40·(-195)
Δ = 31825
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:

$\sqrt{\Delta}=\sqrt{31825}=\sqrt{25*1273}=\sqrt{25}*\sqrt{1273}=5\sqrt{1273}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{1273}}{2*40}=\frac{25-5\sqrt{1273}}{80}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{1273}}{2*40}=\frac{25+5\sqrt{1273}}{80}
$