Assuming a,b, and c are constant it could be of this form, have you solved your charateristic equation yet? What did you get?
Yes, a,b and c are constants, sorry I forgot to put that in.
It becomes a quadratic equation:
r^2 + ar + (bc)^2 = 0.
The quadratic formula gives
r = [-a + sqrt(a^2 - 4(bc)^2)]/2 and
r = [-a - sqrt(a^2 - 4(bc)^2)]/2.
I note that there will be two independent solutions when the discrimant is positive, that is, when
a^2 - 4(bc)^2 > 0, or
a^2 > 4(bc)^2, or
|a| > |2bc|