(4y-15)(3y+15)=180

Solution for (4y-15)(3y+15)=180 equation:

(4y-15)(3y+15)=180

We move all terms to the left:

(4y-15)(3y+15)-(180)=0

We multiply parentheses ..

(+12y^2+60y-45y-225)-180=0

We get rid of parentheses

12y^2+60y-45y-225-180=0

We add all the numbers together, and all the variables

12y^2+15y-405=0

a = 12; b = 15; c = -405;
Δ = b2-4ac
Δ = 152-4·12·(-405)
Δ = 19665
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:

$\sqrt{\Delta}=\sqrt{19665}=\sqrt{9*2185}=\sqrt{9}*\sqrt{2185}=3\sqrt{2185}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{2185}}{2*12}=\frac{-15-3\sqrt{2185}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{2185}}{2*12}=\frac{-15+3\sqrt{2185}}{24}
$