Find the intersection points between the graphs y=2x+5 and y=x^2-9.

To do this, first draw a sketch of both graphs to see roughly what kind of result we should expect to get. We know that at the intersection points, the values of x and y for both graphs must be equal. so set both graphs equal to each other and we get

2x+5=x^2-9

rearranging this equation we then get

0=x^2-2x-14

We then use the quadratic formula to get values for x, for which you get 

x=1+squ. root(15) and x=1- squ. root(15) .          (sorry i didn't know how to insert squ. root symbol)

we then substitute both values into either equation (since we're looking at intersection points) and we get

y=7+ 2squ root(15) and y=7-2squ root(15).