2/3n+1=3/5n

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

2/3n+1=3/5n

We move all terms to the left:

2/3n+1-(3/5n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

2/3n-(+3/5n)+1=0

We get rid of parentheses

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

We calculate fractions


10n/15n^2+(-9n)/15n^2+1=0

We multiply all the terms by the denominator


10n+(-9n)+1*15n^2=0

Wy multiply elements

15n^2+10n+(-9n)=0

We get rid of parentheses

15n^2+10n-9n=0

We add all the numbers together, and all the variables

15n^2+n=0

a = 15; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·15·0
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*15}=\frac{-2}{30}
=-1/15
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*15}=\frac{0}{30}
=0
$