2/2n=5/3n+1

Solution for 2/2n=5/3n+1 equation:

2/2n=5/3n+1

We move all terms to the left:

2/2n-(5/3n+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

2/2n-5/3n-1=0

We calculate fractions


6n/6n^2+(-10n)/6n^2-1=0

We multiply all the terms by the denominator


6n+(-10n)-1*6n^2=0

Wy multiply elements

-6n^2+6n+(-10n)=0

We get rid of parentheses

-6n^2+6n-10n=0

We add all the numbers together, and all the variables

-6n^2-4n=0

a = -6; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-6)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-6}=\frac{0}{-12}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-6}=\frac{8}{-12}
=-2/3
$