$f$ be a function satisfying $2f(x)+3f(-x)=x^2+5x$. Find $f(7)$
[list=1]
[*] $-\frac{105}{4}$


[*] $-\frac{126}{5}$


[*] $-\frac{120}{7}$


[*] $-\frac{132}{7}$
[/list]
1. Given the function equation:
   \[
   2f(x) + 3f(-x) = x^2 + 5x
   \]
   We will first substitute \( x \) with \( -x \) to obtain a second equation.

2. Substituting \( x \mapsto -x \):
   \[
   2f(-x) + 3f(x) = x^2 - 5x
   \]

3. Now we have the system of equations:
   \[
   \begin{cases}
   2f(x) + 3f(-x) = x^2 + 5x \\
   2f(-x) + 3f(x) = x^2 - 5x
   \end{cases}
   \]

4. To eliminate \( f(-x) \), we can multiply the first equation by 3 and the second equation by 2:
   \[
   \begin{cases}
   6f(x) + 9f(-x) = 3x^2 + 15x \\
   4f(-x) + 6f(x) = 2x^2 - 10x
   \end{cases}
   \]

5. Subtract the second equation from the first:
   \[
   (6f(x) + 9f(-x)) - (4f(-x) + 6f(x)) = (3x^2 + 15x) - (2x^2 - 10x)
   \]
   Simplifying, we get:
   \[
   3f(-x) - 4f(-x) = x^2 + 25x
   \]
   \[
   5f(-x) = x^2 + 25x
   \]
   \[
   f(-x) = \frac{1}{5}x^2 + 5x
   \]

6. Substitute \( f(-x) \) back into the original equation:
   \[
   2f(x) + 3\left(\frac{1}{5}x^2 + 5x\right) = x^2 + 5x
   \]
   Simplify:
   \[
   2f(x) + \frac{3}{5}x^2 + 15x = x^2 + 5x
   \]
   \[
   2f(x) = x^2 + 5x - \frac{3}{5}x^2 - 15x
   \]
   \[
   2f(x) = \left(1 - \frac{3}{5}\right)x^2 + (5x - 15x)
   \]
   \[
   2f(x) = \frac{2}{5}x^2 - 10x
   \]
   \[
   f(x) = \frac{1}{5}x^2 - 5x
   \]

7. Now, we need to find \( f(7) \):
   \[
   f(7) = \frac{1}{5}(7^2) - 5(7)
   \]
   \[
   f(7) = \frac{1}{5}(49) - 35
   \]
   \[
   f(7) = \frac{49}{5} - 35
   \]
   \[
   f(7) = \frac{49}{5} - \frac{175}{5}
   \]
   \[
   f(7) = \frac{49 - 175}{5}
   \]
   \[
   f(7) = \frac{-126}{5}
   \]

The final answer is \(\boxed{-\frac{126}{5}}\)