6y(-3y-18)=12

Solution for 6y(-3y-18)=12 equation:

6y(-3y-18)=12

We move all terms to the left:

6y(-3y-18)-(12)=0

We multiply parentheses

-18y^2-108y-12=0

a = -18; b = -108; c = -12;
Δ = b2-4ac
Δ = -1082-4·(-18)·(-12)
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-60\sqrt{3}}{2*-18}=\frac{108-60\sqrt{3}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+60\sqrt{3}}{2*-18}=\frac{108+60\sqrt{3}}{-36}
$