The domain is the set of allowable x-values. You have been given a rational function. In particular, you have been given a function which has x's in the denominator. Think about what you cannot do in a fraction, what you cannot divide by....
For worked examples of how to find domains, please review this page
To solve, you'll need to find the zeroes of the denominator. The quadratic does factor
, but you can also use the Quadratic Formula
, if you prefer.