3y(2y+3)=2y+3

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

3y(2y+3)=2y+3

We move all terms to the left:

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

We multiply parentheses

6y^2+9y-(2y+3)=0

We get rid of parentheses

6y^2+9y-2y-3=0

We add all the numbers together, and all the variables

6y^2+7y-3=0

a = 6; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·6·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*6}=\frac{-18}{12}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*6}=\frac{4}{12}
=1/3
$