1+1/5n=3/n

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

1+1/5n=3/n

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


n/5n^2+(-15n)/5n^2+1=0

We multiply all the terms by the denominator


n+(-15n)+1*5n^2=0

Wy multiply elements

5n^2+n+(-15n)=0

We get rid of parentheses

5n^2+n-15n=0

We add all the numbers together, and all the variables

5n^2-14n=0

a = 5; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·5·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*5}=\frac{0}{10}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*5}=\frac{28}{10}
=2+4/5
$