2. If $a-2$ is a positive integer and a divisor of $3 a^{2}-2 a+10$, then the sum of all possible values of $a$ is $\qquad$ .
2.51.
$$
\begin{array}{l}
\text { Given } \frac{3 a^{2}-2 a+10}{a-2} \\
=\frac{\left(3 a^{2}-6 a\right)+(4 a-8)+18}{a-2} \\
=3 a+4+\frac{18}{a-2}(a \neq 2),
\end{array}
$$

we know that $a-2$ must be a divisor of 18.
Thus, $a=3,4,5,8,11,20$.
Therefore, the sum of all possible values of $a$ is
$$
3+4+5+8+11+20=51 \text {. }
$$