2n-3/2n=16

Solution for 2n-3/2n=16 equation:

2n-3/2n=16

We move all terms to the left:

2n-3/2n-(16)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


2n*2n-16*2n-3=0

Wy multiply elements

4n^2-32n-3=0

a = 4; b = -32; c = -3;
Δ = b2-4ac
Δ = -322-4·4·(-3)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{67}}{2*4}=\frac{32-4\sqrt{67}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{67}}{2*4}=\frac{32+4\sqrt{67}}{8}
$