100/n=10n=

Solution for 100/n=10n= equation:

100/n=10n=

We move all terms to the left:

100/n-(10n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-10n+100/n=0

We multiply all the terms by the denominator


-10n*n+100=0

Wy multiply elements

-10n^2+100=0

a = -10; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-10)·100
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*-10}=\frac{0-20\sqrt{10}}{-20}
=-\frac{20\sqrt{10}}{-20}
=-\frac{\sqrt{10}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*-10}=\frac{0+20\sqrt{10}}{-20}
=\frac{20\sqrt{10}}{-20}
=\frac{\sqrt{10}}{-1}
$