2n=2/n+0.1

Solution for 2n=2/n+0.1 equation:

2n=2/n+0.1

We move all terms to the left:

2n-(2/n+0.1)=0


Domain of the equation: n+0.1)!=0

n∈R


We get rid of parentheses

2n-2/n-0.1=0

We multiply all the terms by the denominator


2n*n-(0.1)*n-2=0

We multiply parentheses

2n*n-0.1n-2=0

Wy multiply elements

2n^2-0.1n-2=0

a = 2; b = -0.1; c = -2;
Δ = b2-4ac
Δ = -0.12-4·2·(-2)
Δ = 16.01
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.1)-\sqrt{16.01}}{2*2}=\frac{0.1-\sqrt{16.01}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{16.01}}{2*2}=\frac{0.1+\sqrt{16.01}}{4}
$