2n-11/2n=16

Solution for 2n-11/2n=16 equation:

2n-11/2n=16

We move all terms to the left:

2n-11/2n-(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-11=0

Wy multiply elements

4n^2-32n-11=0

a = 4; b = -32; c = -11;
Δ = b2-4ac
Δ = -322-4·4·(-11)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-20\sqrt{3}}{2*4}=\frac{32-20\sqrt{3}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+20\sqrt{3}}{2*4}=\frac{32+20\sqrt{3}}{8}
$