2n-1+1/2n=16

Solution for 2n-1+1/2n=16 equation:

2n-1+1/2n=16

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

2n+1/2n-17=0

We multiply all the terms by the denominator


2n*2n-17*2n+1=0

Wy multiply elements

4n^2-34n+1=0

a = 4; b = -34; c = +1;
Δ = b2-4ac
Δ = -342-4·4·1
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{285}}{2*4}=\frac{34-2\sqrt{285}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{285}}{2*4}=\frac{34+2\sqrt{285}}{8}
$