1/2n+6=2/3n

Solution for 1/2n+6=2/3n equation:

1/2n+6=2/3n

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2n-2/3n+6=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

36n^2+3n+(-4n)=0

We get rid of parentheses

36n^2+3n-4n=0

We add all the numbers together, and all the variables

36n^2-1n=0

a = 36; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·36·0
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*36}=\frac{0}{72}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*36}=\frac{2}{72}
=1/36
$