Factoring

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).

10x^2 - 19x + 6
= (5x - 2)(2x - 3)

hope it helps