when x ε [I, I+1) where I is a positive integer...
For any negative x there is no solution
for x ε [0,1) ... [x]=0 so no solution
for x ε [1,2) ... [x] = 1 so no solution
for x ε [2,3) ... [x]=2 so {x} = 0.5 so, x=2.5
for x ε [3,4) ... [x]=3 so {x} = 0.3 so, x=3.3/o]
for x ε [4,5) ... [x]=4 so {x}=0.25 so x = 4.25
ao basically it is x = n + 1/n where n is positive integer greater than or equal to 2