Recurrence relation advice

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$t_n=5t_{n-1}+6t_{n-2}$

Is the characteristic equation of this correct? This is what I have:

$x$- 5$x$ -6=0

Is this correct?

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Presuming you mean $t_n=5t_{n-1}+6t_{n-2}$ you substitute in $t_n=ax^n$ and you will get $x^2=5x+6$ I don't know what the $=0$s are doing there. If they are real, you have $t_n=0$ and are already done