Note that when a point lies on the x-axis, it has a y-coordinate of 0. So in order to find your roots, we set your quadratic equation equal to 0, i.e.:
First, divide -3 from both sides since we're going to have to factor and it's much easier to deal with no coefficients in front of the :
Now factor the quadratic to get the form: and solve for x by setting and .
This works because when you multiply 2 numbers to get 0, either one or the other or both are equal to 0. So, setting both terms (x-a) and (x-b) equal to 0 will lead you to your x-values that correspond to the y-intercept.