2y(3y+5)=y

Solution for 2y(3y+5)=y equation:

2y(3y+5)=y

We move all terms to the left:

2y(3y+5)-(y)=0

We add all the numbers together, and all the variables

-1y+2y(3y+5)=0

We multiply parentheses

6y^2-1y+10y=0

We add all the numbers together, and all the variables

6y^2+9y=0

a = 6; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·6·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*6}=\frac{-18}{12}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*6}=\frac{0}{12}
=0
$