Question

2[x] = 4{x} + x , where [ ] represents greatest integer function and { } represents fractional part function.

Answer 1

Write $x=n+f$,

where $f$ is a fraction between $0$ and $1$, and $n$ is an integer.

Then your equation is $2n=4f+n+f\Rightarrow n=5f$.

Since $n$ is an integer and $f$ is a fraction

Then $0<=f=n/5<1$.

This implies $0\le n\le 4$ and

$x=n+f=n+\frac{n}{5}=\frac{6n}{5}.$

So,

$x=0,\frac{6}{5},\frac{12}{5},\frac{18}{5},\frac{24}{5}$

Hence, this is the answer.