Depending on your functions, you may be able to use Solve or NSolve or Reduce. Simple example
sol = Solve[x == Cos[x], x, Reals] // N
solX = x /. sol // First
solY = Cos[solX] (* same as solX *)
Plot[{x, Cos[x]}, {x, 0, Pi/2},
Epilog -> {Red, PointSize[Large], Point[{solX, solY}]}]
