2/3n=3+1/2n

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

2/3n=3+1/2n

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-18n^2+4n+(-3n)=0

We get rid of parentheses

-18n^2+4n-3n=0

We add all the numbers together, and all the variables

-18n^2+n=0

a = -18; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-18)·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*-18}=\frac{-2}{-36}
=1/18
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-18}=\frac{0}{-36}
=0
$