6y(2y-3)=6

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

6y(2y-3)=6

We move all terms to the left:

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

We multiply parentheses

12y^2-18y-6=0

a = 12; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·12·(-6)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{17}}{2*12}=\frac{18-6\sqrt{17}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{17}}{2*12}=\frac{18+6\sqrt{17}}{24}
$