If the whole length is equal to 59, then adding the two segments is also equal to 59. That means that (8x-14)+(4x+1)=59. From there you should be able to solve for x, and then plug in x for each of the two lengths. For example, if x was equal to 3 (which it is NOT, so do not use that as the answer), then 8x-14=3*8-14=24-14=10.
Hope this helps!