I am having trouble understanding how to find the x intercept of a problem like
y=x^2-3x-10

Set y=0 and solve the quadratic by using the quadratic formula, factoring, or completing the square.

x^{2}-3x-10=0

I would factor.

The x-intercept is the point (or points) where y = 0. So in the example you gave solve for:

0 = x^2-3x-10.

You can solve this using the quadratic equation - you'll find it hgas two solutions.