2y(3y-6)=18

Solution for 2y(3y-6)=18 equation:

2y(3y-6)=18

We move all terms to the left:

2y(3y-6)-(18)=0

We multiply parentheses

6y^2-12y-18=0

a = 6; b = -12; c = -18;
Δ = b2-4ac
Δ = -122-4·6·(-18)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*6}=\frac{-12}{12}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*6}=\frac{36}{12}
=3
$