I'm struggling to rearrange to find x - simultaneous circle equations

Hi,

I need to rearrange the following in order to find x.

I'm attempting to solve two circle equations simultaneously, I have subtracted one from the other and found y in terms of x, and substituted this back into one of the original equations in order to solve for x... but am not certain how to proceed!

I arrived at this point following this procedure:

Expanding the brackets ->

replacing (-a) with g and (-b) with f (apparently this is convention)->

collect together the non-x and non-y terms ->

gives the general circle equation (I believe!)

One representing each of the two intersecting circles ->

Subtract (2) from (1) ->

Using g, f and c as the results of the subtractions ->

Subtract c and gx and then divide by f ->

Substituting this back into equation (1) gives the equation which I need to solve. (Also at top of post).

I'm uncertain if I'm going about this in the best way, so if anybody has an easier alternative I would be very grateful.

I cannot guarantee the circles will be orthogonal so I cannot use kite geometry.

Any help/advice would be greatly appreciated.