1/3y=y*3

Solution for 1/3y=y*3 equation:

1/3y=y*3

We move all terms to the left:

1/3y-(y*3)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3y-y*3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

-9y^2+1=0

a = -9; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-9)·1
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{-(0)-6}{2*-9}=\frac{-6}{-18}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-9}=\frac{6}{-18}
=-1/3
$