1/5n+3=1/2n

Solution for 1/5n+3=1/2n equation:

1/5n+3=1/2n

We move all terms to the left:

1/5n+3-(1/2n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/5n-(+1/2n)+3=0

We get rid of parentheses

1/5n-1/2n+3=0

We calculate fractions


2n/10n^2+(-5n)/10n^2+3=0

We multiply all the terms by the denominator


2n+(-5n)+3*10n^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

30n^2-3n=0

a = 30; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·30·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*30}=\frac{0}{60}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*30}=\frac{6}{60}
=1/10
$