1/n=n/16n=

Solution for 1/n=n/16n= equation:

1/n=n/16n=

We move all terms to the left:

1/n-(n/16n)=0


Domain of the equation: n!=0

n∈R



Domain of the equation: 16n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/n-(+n/16n)=0

We get rid of parentheses

1/n-n/16n=0

We calculate fractions


(-1n^2)/16n^2+16n/16n^2=0

We multiply all the terms by the denominator


(-1n^2)+16n=0

We get rid of parentheses

-1n^2+16n=0

a = -1; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-1)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-1}=\frac{-32}{-2}
=+16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-1}=\frac{0}{-2}
=0
$