5n=5/n

Solution for 5n=5/n equation:

5n=5/n

We move all terms to the left:

5n-(5/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

5n-(+5/n)=0

We get rid of parentheses

5n-5/n=0

We multiply all the terms by the denominator


5n*n-5=0

Wy multiply elements

5n^2-5=0

a = 5; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·5·(-5)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*5}=\frac{-10}{10}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*5}=\frac{10}{10}
=1
$