Number of solution of equation `[x]^2=x+2{x}` is/are , where [.] and {.} denote the greatest integer and the fractional part functions, respectively

Explanation

`[x]^(2)=x+2{x}`
or `[x]^(2)=[x]+3{x}`
or `{x}=([x]^(2)-[x])/(3)`
or ` 0 le ([x]^(2)-[x])/(3) lt 1`
or `0 le [x]^(2)-[x] lt 3`
or `[x] in ((1-sqrt(13))/(2),0] cup [1,(1-sqrt(13))/(2))`
or `[x] = -1,0,1,2`
or `{x}=(2)/(3),0,0,(2)/(3)` (respectively)
or `x= -(1)/(3),0,1,(8)/(3)`