1/8n=11n=

Solution for 1/8n=11n= equation:

1/8n=11n=

We move all terms to the left:

1/8n-(11n)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R


We add all the numbers together, and all the variables

-11n+1/8n=0

We multiply all the terms by the denominator


-11n*8n+1=0

Wy multiply elements

-88n^2+1=0

a = -88; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-88)·1
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*-88}=\frac{0-4\sqrt{22}}{-176}
=-\frac{4\sqrt{22}}{-176}
=-\frac{\sqrt{22}}{-44}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*-88}=\frac{0+4\sqrt{22}}{-176}
=\frac{4\sqrt{22}}{-176}
=\frac{\sqrt{22}}{-44}
$