y(3y-11)=-3

Solution for y(3y-11)=-3 equation:

y(3y-11)=-3

We move all terms to the left:

y(3y-11)-(-3)=0

We add all the numbers together, and all the variables

y(3y-11)+3=0

We multiply parentheses

3y^2-11y+3=0

a = 3; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·3·3
Δ = 85
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{-(-11)-\sqrt{85}}{2*3}=\frac{11-\sqrt{85}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{85}}{2*3}=\frac{11+\sqrt{85}}{6}
$