(15y-4)(12y-5)=180

Solution for (15y-4)(12y-5)=180 equation:

(15y-4)(12y-5)=180

We move all terms to the left:

(15y-4)(12y-5)-(180)=0

We multiply parentheses ..

(+180y^2-75y-48y+20)-180=0

We get rid of parentheses

180y^2-75y-48y+20-180=0

We add all the numbers together, and all the variables

180y^2-123y-160=0

a = 180; b = -123; c = -160;
Δ = b2-4ac
Δ = -1232-4·180·(-160)
Δ = 130329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{130329}=\sqrt{81*1609}=\sqrt{81}*\sqrt{1609}=9\sqrt{1609}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-123)-9\sqrt{1609}}{2*180}=\frac{123-9\sqrt{1609}}{360}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-123)+9\sqrt{1609}}{2*180}=\frac{123+9\sqrt{1609}}{360}
$