15y(4y-9)-3(4y-9)=0

Solution for 15y(4y-9)-3(4y-9)=0 equation:

15y(4y-9)-3(4y-9)=0

We multiply parentheses

60y^2-135y-12y+27=0

We add all the numbers together, and all the variables

60y^2-147y+27=0

a = 60; b = -147; c = +27;
Δ = b2-4ac
Δ = -1472-4·60·27
Δ = 15129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15129}=123$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-147)-123}{2*60}=\frac{24}{120}
=1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+123}{2*60}=\frac{270}{120}
=2+1/4
$