X=120/17
First observe your triangles and what is needed to be found (or in this case the vale of x).
Now recognize that there are two SIMILAR triangles which are triangle ABC and triangle ABD. You can see this because they are BOTH right triangles and both have the similar angle value of angle A, therefore proven similar by AA congruence.
Now that you know these two triangles are similar you must find your scale factor (how much to multiply on each side in order to get to the given values). To find your scale factor you want to divide (or multiply in some cases) a side length of triangle ABC from triangle ABD because you are REDUCING the length. Since both segments AC and AB are both given as your hypotenuse then you can use those values o find the scale factor. So you would do 8/17 (which is the scale factor).
Now that you have the scale factor you need to find the side that is similar to BD which is BC. Now multiply 15 (BC) by 8/17 to get 120/17.