y/3y-4=y

Solution for y/3y-4=y equation:

y/3y-4=y

We move all terms to the left:

y/3y-4-(y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+y/3y-4=0

We multiply all the terms by the denominator


-1y*3y+y-4*3y=0

We add all the numbers together, and all the variables

y-1y*3y-4*3y=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-3y^2-11y=0

a = -3; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-3)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-3}=\frac{0}{-6}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-3}=\frac{22}{-6}
=-3+2/3
$