If x is real, the expression x+22x2+3x+6  takes all value in the interval:

If the given expression be y , then              2x2y+(3y−1)x+(6y−2)=0If y≠0  then Δ≥0  for real x , i.e., B2−4AC≥0or             −39y2+10y+1≥0or            (13y+1)(3y−1)≤0⇒                   −113≤y≤13If y=0  then x=−2  which is real and this value of y  is included in the above range.