1+1/n=1/7n

Solution for 1+1/n=1/7n equation:

1+1/n=1/7n

We move all terms to the left:

1+1/n-(1/7n)=0


Domain of the equation: n!=0

n∈R



Domain of the equation: 7n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/n-(+1/7n)+1=0

We get rid of parentheses

1/n-1/7n+1=0

We calculate fractions


7n/7n^2+(-n)/7n^2+1=0

We add all the numbers together, and all the variables

7n/7n^2+(-1n)/7n^2+1=0

We multiply all the terms by the denominator


7n+(-1n)+1*7n^2=0

Wy multiply elements

7n^2+7n+(-1n)=0

We get rid of parentheses

7n^2+7n-1n=0

We add all the numbers together, and all the variables

7n^2+6n=0

a = 7; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·7·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*7}=\frac{-12}{14}
=-6/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*7}=\frac{0}{14}
=0
$