Find all real values of $a$ for which the quadratic equation
\[(3 - i) x^2 + (a + 4i) x - 115 + 5i = 0\]has at least one real root.

Enter all the possible values of $a,$ separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all real values of $a$ for which the quadratic equation
\[(3 - i) x^2 + (a + 4i) x - 115 + 5i = 0\]has at least one real root.

Enter all the possible values of $a,$ separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8,-112
Find all real values of $a$ for which the quadratic equation
\[(3 - i) x^2 + (a + 4i) x - 115 + 5i = 0\]has at least one real root.

Enter all the possible values of $a,$ separated by commas.
train