It looks like it's going to have complex roots, but we'll see.

x = (-b ± √ (b² - 4ac))÷ 2a

x = (-9 ± √ (-63))÷ 2

The negative square root confirms my suspicions.

The roots work out to be -4.5 ± (1.5√7)i, where i is √(-1).

If the solutions to the auxiliary equation are complex, they go into the following equation:

λ = c±di ∴ y = e^c (Acosdx + Bsindx), where A and B are arbitrary constants.

For your example, y = e^-4.5 (Acos(1.5√7)x + Bsin(1.5√7)x)