If x is real, the smallest value of the expression $$3x^{2} - 4x + 7$$ is :

$$3x^{2} - 4x + 7$$ is the given quadratic equation
The smallest value of a given quadratic equation $$ax^2 + bx + c = 0$$ occurs at $$ x = \dfrac{-b}{2a}$$
Thus, the smallest value of the given expression will occur at  $$ x = \dfrac{-(-4)}{2*3} = \dfrac{2}{3}$$
Thus, the smallest vale of the given expression is $$3*(\dfrac{2}{3})^2 - 4*(\dfrac{2}{3}) + 7 = \dfrac{17}{3}$$
Hence, option D is the correct answer.