1/10n+5=3/5n

Solution for 1/10n+5=3/5n equation:

1/10n+5=3/5n

We move all terms to the left:

1/10n+5-(3/5n)=0


Domain of the equation: 10n!=0

n!=0/10

n!=0

n∈R



Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/10n-(+3/5n)+5=0

We get rid of parentheses

1/10n-3/5n+5=0

We calculate fractions


5n/50n^2+(-30n)/50n^2+5=0

We multiply all the terms by the denominator


5n+(-30n)+5*50n^2=0

Wy multiply elements

250n^2+5n+(-30n)=0

We get rid of parentheses

250n^2+5n-30n=0

We add all the numbers together, and all the variables

250n^2-25n=0

a = 250; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·250·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*250}=\frac{0}{500}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*250}=\frac{50}{500}
=1/10
$