(8c-5)(6c-3)=180

Solution for (8c-5)(6c-3)=180 equation:

(8c-5)(6c-3)=180

We move all terms to the left:

(8c-5)(6c-3)-(180)=0

We multiply parentheses ..

(+48c^2-24c-30c+15)-180=0

We get rid of parentheses

48c^2-24c-30c+15-180=0

We add all the numbers together, and all the variables

48c^2-54c-165=0

a = 48; b = -54; c = -165;
Δ = b2-4ac
Δ = -542-4·48·(-165)
Δ = 34596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34596}=186$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-186}{2*48}=\frac{-132}{96}
=-1+3/8
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+186}{2*48}=\frac{240}{96}
=2+1/2
$