Quadratic Equation and Inequalities

If $$a \in R$$ and the equation $$- 3{\left( {x - \left[ x \right]} \right)^2} + 2\left( {x - \left[ x \right]} \right) + {a^2} = 0$$ (where [$$x$$] denotes the greater integer $$\le x$$) has no integral solution, then all possible values of a lie in the interval :