(5y-3)(3y+27)=180

Solution for (5y-3)(3y+27)=180 equation:

(5y-3)(3y+27)=180

We move all terms to the left:

(5y-3)(3y+27)-(180)=0

We multiply parentheses ..

(+15y^2+135y-9y-81)-180=0

We get rid of parentheses

15y^2+135y-9y-81-180=0

We add all the numbers together, and all the variables

15y^2+126y-261=0

a = 15; b = 126; c = -261;
Δ = b2-4ac
Δ = 1262-4·15·(-261)
Δ = 31536
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:

$\sqrt{\Delta}=\sqrt{31536}=\sqrt{144*219}=\sqrt{144}*\sqrt{219}=12\sqrt{219}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-12\sqrt{219}}{2*15}=\frac{-126-12\sqrt{219}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+12\sqrt{219}}{2*15}=\frac{-126+12\sqrt{219}}{30}
$