3(3y-1)3(2y)=5

Solution for 3(3y-1)3(2y)=5 equation:

3(3y-1)3(2y)=5

We move all terms to the left:

3(3y-1)3(2y)-(5)=0

We multiply parentheses

288y^2-96y-5=0

a = 288; b = -96; c = -5;
Δ = b2-4ac
Δ = -962-4·288·(-5)
Δ = 14976
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:

$\sqrt{\Delta}=\sqrt{14976}=\sqrt{576*26}=\sqrt{576}*\sqrt{26}=24\sqrt{26}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-24\sqrt{26}}{2*288}=\frac{96-24\sqrt{26}}{576}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+24\sqrt{26}}{2*288}=\frac{96+24\sqrt{26}}{576}
$