1/2n=21-2n

Solution for 1/2n=21-2n equation:

1/2n=21-2n

We move all terms to the left:

1/2n-(21-2n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

1/2n-(-2n+21)=0

We get rid of parentheses

1/2n+2n-21=0

We multiply all the terms by the denominator


2n*2n-21*2n+1=0

Wy multiply elements

4n^2-42n+1=0

a = 4; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·4·1
Δ = 1748
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:

$\sqrt{\Delta}=\sqrt{1748}=\sqrt{4*437}=\sqrt{4}*\sqrt{437}=2\sqrt{437}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{437}}{2*4}=\frac{42-2\sqrt{437}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{437}}{2*4}=\frac{42+2\sqrt{437}}{8}
$