Subtract \({x - 5 \over x + 5} \) from both sides: \({9 \over x + 5} = {x-5 \over 2x}\)
Cross multiply: \(18x = x^2 - 25\)
Subtract 18x from both sides: \(x^2 - 18x - 25 = 0\)
Use the quadratic formula: \(x = \color{brown}\boxed{{9 \pm \sqrt{106} }}\)