1/2n-15/4n=511/16

Solution for 1/2n-15/4n=511/16 equation:

1/2n-15/4n=511/16

We move all terms to the left:

1/2n-15/4n-(511/16)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

1/2n-15/4n-(+511/16)=0

We get rid of parentheses

1/2n-15/4n-511/16=0

We calculate fractions


(-16352n^2)/128n^2+64n/128n^2+(-480n)/128n^2=0

We multiply all the terms by the denominator


(-16352n^2)+64n+(-480n)=0

We get rid of parentheses

-16352n^2+64n-480n=0

We add all the numbers together, and all the variables

-16352n^2-416n=0

a = -16352; b = -416; c = 0;
Δ = b2-4ac
Δ = -4162-4·(-16352)·0
Δ = 173056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{173056}=416$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-416)-416}{2*-16352}=\frac{0}{-32704}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-416)+416}{2*-16352}=\frac{832}{-32704}
=-13/511
$