5n+0.1111111111111=5/n

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Solution for 5n+0.1111111111111=5/n equation: 



5n+0.1111111111111=5/n

We move all terms to the left:

5n+0.1111111111111-(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)+0.1111111111111=0

We get rid of parentheses

5n-5/n+0.1111111111111=0

We multiply all the terms by the denominator


5n*n+(0.1111111111111)*n-5=0

We multiply parentheses

5n*n+0.1111111111111n-5=0

Wy multiply elements

5n^2+0.1111111111111n-5=0

a = 5; b = 0.1111111111111; c = -5;
Δ = b2-4ac
Δ = 0.11111111111112-4·5·(-5)
Δ = 100.01234567901
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{-(0.1111111111111)-\sqrt{100.01234567901}}{2*5}=\frac{-0.1111111111111-\sqrt{100.01234567901}}{10}
$


$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.1111111111111)+\sqrt{100.01234567901}}{2*5}=\frac{-0.1111111111111+\sqrt{100.01234567901}}{10}
$

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