1/2n=2/3n+1

Solution for 1/2n=2/3n+1 equation:

1/2n=2/3n+1

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



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

n∈R


We get rid of parentheses

1/2n-2/3n-1=0

We calculate fractions


3n/6n^2+(-4n)/6n^2-1=0

We multiply all the terms by the denominator


3n+(-4n)-1*6n^2=0

Wy multiply elements

-6n^2+3n+(-4n)=0

We get rid of parentheses

-6n^2+3n-4n=0

We add all the numbers together, and all the variables

-6n^2-1n=0

a = -6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-6)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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