What is this strange notation in the output of Wolfram Alpha? For some reason I need to find the values of two positive integers $k$ and $x$ such that:
$$
k x^3 (2 x + 1)^3>2 (k + 1) (x + 1)^2 (2 x^4 + 2 x^3 + 3 x^2 + 2 x + 1).
$$
Inputting this in Wolfram Alpha gives the following strange result (among others):

$$ k>1, x>Root[\#1^6 (4 k - 4) - 12 \#1^5 + \#1^4 (-12 k - 18) + \#1^3
> (-19 k - 20) + \#1^2 (-16 k - 16) + \#1 (-8 k - 8) - 2 k - 2\&, 2] $$

What does this mean? What is the role of the symbols $\#$ and $\&$?

Using a command like
RegionPlot[
 $k x^3 (2 x + 1)^3 - 
   2 (k + 1) (x + 1)^2 (2 x^4 + 2 x^3 + 3 x^2 + 2 x + 1) > 0$, {$k$, 0, 
  10}, {$x$, 0, 10}]
You will obtain an useful plot

