Trey, Amelia, and Cho are discussing the solution set to the equation x^2+9=45 .

To solve the equation \( x^2 + 9 = 45 \), we first isolate \( x^2 \):

\[
x^2 + 9 = 45
\]

Subtract 9 from both sides:

\[
x^2 = 45 - 9
\]

\[
x^2 = 36
\]

Next, we take the square root of both sides:

\[
x = \pm \sqrt{36}
\]

This gives us:

\[
x = 6 \quad \text{or} \quad x = -6
\]

Thus, the solution set is \( \{-6, 6\} \).

Amelia is the only one who correctly identifies the solution set as \( \{-6, 6\} \).

Therefore, the correct answer is:

**Amelia**