1/2n-2/16n=3/8

Solution for 1/2n-2/16n=3/8 equation:

1/2n-2/16n=3/8

We move all terms to the left:

1/2n-2/16n-(3/8)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 16n!=0

n!=0/16

n!=0

n∈R


We add all the numbers together, and all the variables

1/2n-2/16n-(+3/8)=0

We get rid of parentheses

1/2n-2/16n-3/8=0

We calculate fractions


(-96n^2)/2048n^2+1024n/2048n^2+(-256n)/2048n^2=0

We multiply all the terms by the denominator


(-96n^2)+1024n+(-256n)=0

We get rid of parentheses

-96n^2+1024n-256n=0

We add all the numbers together, and all the variables

-96n^2+768n=0

a = -96; b = 768; c = 0;
Δ = b2-4ac
Δ = 7682-4·(-96)·0
Δ = 589824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{589824}=768$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(768)-768}{2*-96}=\frac{-1536}{-192}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(768)+768}{2*-96}=\frac{0}{-192}
=0
$