Question 258575
THere are at least two ways to solve this. Here is one of them: What we have here is a circle in disguise with center (4,-3) and radius 5. Its equation is
{{{(x-4)^2+(y+3)^2 = 5^2}}}
since we want coordinates on the x-axis, set y  = 0 and solve for x like this
{{{(x-4)^2+(0+3)^2 = 5^2}}}
{{{(x-4)^2+9 = 25}}}
{{{(x-4)^2=16}}}
take a square root to get
x-4 = +-5
So, 
x = 9
OR
x = -1
This means that (9,0) and (-1,0) is 5 units from (4,-3)