(2y+3)3y=8

Solution for (2y+3)3y=8 equation:

(2y+3)3y=8

We move all terms to the left:

(2y+3)3y-(8)=0

We multiply parentheses

6y^2+9y-8=0

a = 6; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·6·(-8)
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{273}}{2*6}=\frac{-9-\sqrt{273}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{273}}{2*6}=\frac{-9+\sqrt{273}}{12}
$