Find a formula for $\displaystyle Tn$ if $\displaystyle Tn = 3Tn-2 + 5$, with initial conditions

$\displaystyle T0 = 1$ and$\displaystyle T1 = 2$.

I have $\displaystyle x^3-3x-5 = 0$ for my characteristics equation and I'm not sure if it's right or not. If it is right, how do I find the roots??