Floor and Fractional Part Equation

Let $f(x) = \lfloor x \rfloor$ (floor function) and $g(x) = \{x\} = x - \lfloor x \rfloor$ (fractional part function). Find the sum all possible values of $x$ such that $f(x) - g(x) = 4.5$. The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.