Dishwashing mathmatical help needed!

Hey, I'm new here, because I dont no where else to go with my bemusing problem...

I'm taking part in a Science Technology Engineering and Mathmatics course, but this problem which I came across is something I haven't covered within my skillset yet...

Firstly, the basic problem is about Re-usable cups vs Disposable cups, but I'm having problems doing a certian energy calculation.

I worked out that the energy cost for a re-usable cup would be:

*n*/*x* + *x*(r) with *x* being number of uses/washes, r being the energy to wash a cup in a dishwasher in joules (total dishwasher energy/total number of cups) and *n* being the production energy, also in joules. However, I know some of these values, making the problem:

*6,300,000*/*x* + *x*(64,800) = the total energy (which I will call T)

Now what I got stuck on is this...

I know it takes 310,000 joules of energy to make a plastic disposable cup. I want to find out how many times I need to use and wash the cup to get a payback time on my re-using.

So I got T=*6,300,000*/*x* + *x*(64,800)

But with T being 310,000

310,000 = *6,300,000*/*x* + *64800x*

But how do I find x?

I end up with:

*6,300,000*/*x* + *x*(64,800) = 310,000

*6,300,000*/*x* + 64,800x = 310,000

64,800x + *6,300,000*/*x* = 310,000

64,800x = 310,000 - *6,300,000*/*x*

and I just stop...

Have I gone wrong somewhere?