6(2y-1)(3y)=3

Solution for 6(2y-1)(3y)=3 equation:

6(2y-1)(3y)=3

We move all terms to the left:

6(2y-1)(3y)-(3)=0

We multiply parentheses

36y^2-18y-3=0

a = 36; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·36·(-3)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{21}}{2*36}=\frac{18-6\sqrt{21}}{72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{21}}{2*36}=\frac{18+6\sqrt{21}}{72}
$