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To solve the equation \(x^2 + 9 = 45\), we first isolate \(x^2\):
\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]
Next, we take the square root of both sides to find \(x\):
\[
x = \pm \sqrt{36}
\]
\[
x = \pm 6
\]
The solution set is \(\{-6, 6\}\).
So, the correct person who found the solution set is **Amelia**.