2y(y-6)-3(y-4)=y

Solution for 2y(y-6)-3(y-4)=y equation:

2y(y-6)-3(y-4)=y

We move all terms to the left:

2y(y-6)-3(y-4)-(y)=0

We add all the numbers together, and all the variables

-1y+2y(y-6)-3(y-4)=0

We multiply parentheses

2y^2-1y-12y-3y+12=0

We add all the numbers together, and all the variables

2y^2-16y+12=0

a = 2; b = -16; c = +12;
Δ = b2-4ac
Δ = -162-4·2·12
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{10}}{2*2}=\frac{16-4\sqrt{10}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{10}}{2*2}=\frac{16+4\sqrt{10}}{4}
$