5n+0.1=5/n

Solution for 5n+0.1=5/n equation:

5n+0.1=5/n

We move all terms to the left:

5n+0.1-(5/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-(+5/n)+0.1=0

We get rid of parentheses

5n-5/n+0.1=0

We multiply all the terms by the denominator


5n*n+(0.1)*n-5=0

We multiply parentheses

5n*n+0.1n-5=0

Wy multiply elements

5n^2+0.1n-5=0

a = 5; b = 0.1; c = -5;
Δ = b2-4ac
Δ = 0.12-4·5·(-5)
Δ = 100.01
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.1)-\sqrt{100.01}}{2*5}=\frac{-0.1-\sqrt{100.01}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.1)+\sqrt{100.01}}{2*5}=\frac{-0.1+\sqrt{100.01}}{10}
$