3((1/3y)+1)-y=2

Solution for 3((1/3y)+1)-y=2 equation:

3((1/3y)+1)-y=2

We move all terms to the left:

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


Domain of the equation: 3y)+1)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3y^2-6y=0

a = -3; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-3)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-3}=\frac{0}{-6}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-3}=\frac{12}{-6}
=-2
$