2n-(1/n)=100

Solution for 2n-(1/n)=100 equation:

2n-(1/n)=100

We move all terms to the left:

2n-(1/n)-(100)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

2n-(+1/n)-100=0

We get rid of parentheses

2n-1/n-100=0

We multiply all the terms by the denominator


2n*n-100*n-1=0

We add all the numbers together, and all the variables

-100n+2n*n-1=0

Wy multiply elements

2n^2-100n-1=0

a = 2; b = -100; c = -1;
Δ = b2-4ac
Δ = -1002-4·2·(-1)
Δ = 10008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10008}=\sqrt{36*278}=\sqrt{36}*\sqrt{278}=6\sqrt{278}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-6\sqrt{278}}{2*2}=\frac{100-6\sqrt{278}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+6\sqrt{278}}{2*2}=\frac{100+6\sqrt{278}}{4}
$