1/8n=12n=

Solution for 1/8n=12n= equation:

1/8n=12n=

We move all terms to the left:

1/8n-(12n)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R


We add all the numbers together, and all the variables

-12n+1/8n=0

We multiply all the terms by the denominator


-12n*8n+1=0

Wy multiply elements

-96n^2+1=0

a = -96; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-96)·1
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*-96}=\frac{0-8\sqrt{6}}{-192}
=-\frac{8\sqrt{6}}{-192}
=-\frac{\sqrt{6}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*-96}=\frac{0+8\sqrt{6}}{-192}
=\frac{8\sqrt{6}}{-192}
=\frac{\sqrt{6}}{-24}
$