Do you know the Rational Roots Theorem? You could dream up possible rational roots by writing them in the form
plus or minus {1,2, 3,6} OVER plus or minus {1,2,5,10}. For example, 3/10 is rational and just might be a rational root. Next, determine whether or not this is a rational root here thru synthetic division.
If you do not know this theorem, consider using one of the following:
quadratic formula
completing the square
graphing (look for the x-values at which the parabolic graph here crosses the x-axis).