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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+3y^2-18y+2y-12)-3y=0

We get rid of parentheses

3y^2-18y+2y-3y-12=0

We add all the numbers together, and all the variables

3y^2-19y-12=0

a = 3; b = -19; c = -12;
Δ = b2-4ac
Δ = -192-4·3·(-12)
Δ = 505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{505}}{2*3}=\frac{19-\sqrt{505}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{505}}{2*3}=\frac{19+\sqrt{505}}{6}
$