To fill in the blank with a mathematical operation between the numbers \(-2\) and \(\frac{9}{20}\) such that the equation balances with the result being \(-2\), we can see:
\[ -2 , ? , \frac{9}{20} = -2 \]
This implies that the operation should not change the value of \(-2\).
The correct operation to use here is:
\[ -2 + \frac{9}{20} = -2 \]
However, if you want the expression to equal \(-2\), we need the operation to effectively negate the addition of \(\frac{9}{20}\). The operation is a subtraction:
\[ -2 - \frac{9}{20} = -2 \]
Thus, the answer is:
\[ -2 , - , \frac{9}{20} \]