What are the equations of asymptotes of the graph of the function f(x)=3x^2-2x-1 / x^2+3x-10

Please use parentheses around numerator and denominator here to reduce the chances of mis-reading your post.  Better yet, write the given function vertically:

          3x^2-2x-1  
 f(x)=
          x^2+3x-10

horiz. asy.:  Find the limit of 3x^2 / x^2 as x grows large without bound.  It is 3.
Thus, the horiz. asy. is y = 3.

Vert. asymptotes:  Factor the denominator, set the factors = to 0 and solve the resulting equations for x:  x^2 + 3x - 10 = (x+5)(x-2).  So, x=-5 and x=2 are your vertical asymptotes.