3(2y+3)y=3

Solution for 3(2y+3)y=3 equation:

3(2y+3)y=3

We move all terms to the left:

3(2y+3)y-(3)=0

We multiply parentheses

6y^2+9y-3=0

a = 6; b = 9; c = -3;
Δ = b2-4ac
Δ = 92-4·6·(-3)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*6}=\frac{-9-3\sqrt{17}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*6}=\frac{-9+3\sqrt{17}}{12}
$