1/2n-1/5n=3

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

1/2n-1/5n=3

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-30n^2+5n-2n=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{-6}{-60}
=1/10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-30}=\frac{0}{-60}
=0
$