16/n=8n=

Solution for 16/n=8n= equation:

16/n=8n=

We move all terms to the left:

16/n-(8n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-8n+16/n=0

We multiply all the terms by the denominator


-8n*n+16=0

Wy multiply elements

-8n^2+16=0

a = -8; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-8)·16
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{2}}{2*-8}=\frac{0-16\sqrt{2}}{-16}
=-\frac{16\sqrt{2}}{-16}
=-\frac{\sqrt{2}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{2}}{2*-8}=\frac{0+16\sqrt{2}}{-16}
=\frac{16\sqrt{2}}{-16}
=\frac{\sqrt{2}}{-1}
$