jmc

First we bring $x$ to the left side to get $$x^2-4x+9=41.$$We notice that the left side is almost the square $(x-2{)}^2=x^2-4x+4$. Subtracting 5 from both sides lets us complete the square on the left-hand side, $$x^2-4x+4=36,$$so $$(x-2{)}^2=6^2.$$Therefore $x=2\pm 6$. The positive difference between these solutions is $8-(-4)=\boxed{12}$.