1.5y(3y-15)=27

Solution for 1.5y(3y-15)=27 equation:

1.5y(3y-15)=27

We move all terms to the left:

1.5y(3y-15)-(27)=0

We multiply parentheses

3y^2-15y-27=0

a = 3; b = -15; c = -27;
Δ = b2-4ac
Δ = -152-4·3·(-27)
Δ = 549
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:

$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{61}}{2*3}=\frac{15-3\sqrt{61}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{61}}{2*3}=\frac{15+3\sqrt{61}}{6}
$