3y(3y-4)=5

Solution for 3y(3y-4)=5 equation:

3y(3y-4)=5

We move all terms to the left:

3y(3y-4)-(5)=0

We multiply parentheses

9y^2-12y-5=0

a = 9; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·9·(-5)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*9}=\frac{-6}{18}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*9}=\frac{30}{18}
=1+2/3
$