2. (15 points) Let $f(x)=x^{2}-5 x+2020$. Solve the equation $f(3-x)=f(3 x-1)$
Solution: Let the equation be of the form $f(a)=f(b)$, we get:

$a^{2}-5 a+2020=b^{2}-5 b+2020$

$a^{2}-b^{2}-5 a+5 b=0$

$(a-b)(a+b-5)=0$

The product of two factors is zero if at least one of the factors is zero. Therefore, $a=b$ or $a+b=5$.

$\left[\begin{array}{l}a=b \\ a+b=5\end{array} \Leftrightarrow\left[\begin{array}{l}3-x=3 x-1 \\ 3-x+3 x-1=5\end{array} \Leftrightarrow\left[\begin{array}{l}x=1 \\ x=1.5\end{array}\right.\right.\right.$

Answer: $\{1.5$ and 1$\}$.

## Criteria.

| Points | Conditions for awarding |
| :---: | :---: |
| 15 | Correct answer obtained with justification |
| 10 | Incorrect answer due to arithmetic error |
| 0 | Solution does not meet any of the above conditions |