2n-1/2n=63

Solution for 2n-1/2n=63 equation:

2n-1/2n=63

We move all terms to the left:

2n-1/2n-(63)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


2n*2n-63*2n-1=0

Wy multiply elements

4n^2-126n-1=0

a = 4; b = -126; c = -1;
Δ = b2-4ac
Δ = -1262-4·4·(-1)
Δ = 15892
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:

$\sqrt{\Delta}=\sqrt{15892}=\sqrt{4*3973}=\sqrt{4}*\sqrt{3973}=2\sqrt{3973}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3973}}{2*4}=\frac{126-2\sqrt{3973}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3973}}{2*4}=\frac{126+2\sqrt{3973}}{8}
$