How To Solve X^2=14x+40/x^2-100=x+4/x-10?

It seems likely you are asking about how to simplify this. (Please note the parentheses are necessary to make this mean what you want it to mean.)
(x² -14x +40)/(x² -100)

Both the numerator and the denominator can be factored.
(x² -14x +40)/(x² -100) = ((x+4)(x+10))/((x-10)(x+10))

The terms (x+10)/(x+10) have a value of 1, so this expression is equivalent to
  = ((x+4)/(x-10))*((x+10)/(x+10)) = ((x+4)/(x-10))*1
  = (x+4)/(x-10)