y(12-7y)=3y

Solution for y(12-7y)=3y equation:

y(12-7y)=3y

We move all terms to the left:

y(12-7y)-(3y)=0

We add all the numbers together, and all the variables

y(-7y+12)-3y=0

We add all the numbers together, and all the variables

-3y+y(-7y+12)=0

We multiply parentheses

-7y^2-3y+12y=0

We add all the numbers together, and all the variables

-7y^2+9y=0

a = -7; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-7)·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*-7}=\frac{-18}{-14}
=1+2/7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-7}=\frac{0}{-14}
=0
$