Many thanks for the comprehensive explanation Marco.

Hi,

there is a clue in the error message.

{FindRoot[y214862+2y21486-name,{y$21486,0}]}

FindRoot attempts to find a root numerically. As you see the error message says that it fails to do so, because there is the variable y (with the $21486, because of the localisation of Module), and the variable: name. That cannot work. Solve uses other methods and in particular symbolic solutions which makes it work in this case (it doesn't care that name is substituted later.

This is basically a combination of (i) when are the variables substituted by numbers and (ii) do you use symbolics or numerics, I would think.

Best wishes, Marco

Hi,

this works:

Clear[del]
del[x_] := 
 Module[{y, dP, res, OP}, 
  res := {y} /. FindRoot[y^2 + 2 y - x, {y, 0}];
  OP := res[[1]];
  dP := OP + 1;
  Nest[(# + dP/#)/2 &, 1.5, 2]]
del[name /. name -> 3]

Of course,

del[3]

is more concise.

Cheers,

Marco