y(3y-1)-3(2y)=12

Solution for y(3y-1)-3(2y)=12 equation:

y(3y-1)-3(2y)=12

We move all terms to the left:

y(3y-1)-3(2y)-(12)=0

We add all the numbers together, and all the variables

-32y+y(3y-1)-12=0

We multiply parentheses

3y^2-32y-1y-12=0

We add all the numbers together, and all the variables

3y^2-33y-12=0

a = 3; b = -33; c = -12;
Δ = b2-4ac
Δ = -332-4·3·(-12)
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{137}}{2*3}=\frac{33-3\sqrt{137}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{137}}{2*3}=\frac{33+3\sqrt{137}}{6}
$