Solving for x ? [differential equation]

Hello,

I'm stuck with this equation and I can't figure out a way how to solve for t..

So I got the solution of a differential equation(complex roots), and now I need to find the values of t for which y=3.5

3.5 = 12e^(-αt)*cos(ω t) - 12α/ω*e^(-αt)*sin(ω t)

α and ω are constants, I tried changing it to the exponential form, cosine form but it didn't help.

In fact what I need is the time intervals for which y(t) > 3.5

Any tips or advice how to do it ?

Thanks !