5n=8/n

Solution for 5n=8/n equation:

5n=8/n

We move all terms to the left:

5n-(8/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

5n-(+8/n)=0

We get rid of parentheses

5n-8/n=0

We multiply all the terms by the denominator


5n*n-8=0

Wy multiply elements

5n^2-8=0

a = 5; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·5·(-8)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*5}=\frac{0-4\sqrt{10}}{10}
=-\frac{4\sqrt{10}}{10}
=-\frac{2\sqrt{10}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*5}=\frac{0+4\sqrt{10}}{10}
=\frac{4\sqrt{10}}{10}
=\frac{2\sqrt{10}}{5}
$