Plokite_Wolf described your problem well, and I was having the same at first (I was stuck during hours too, not understanding what I was doing wrong) : in Be.HexEditor, click on "Find", here, you select "Hex" (and not "Text"), and now you must put the numbers you want to look at, by hand, one after the other (if you're looking for 58 02 00 00 68 20 03 00 00, type yourself 580200006820030000 : the spaces between numbers will be automatically added because you're in hex mode)(a copy/past from the value doesn't work because it convert/calculate the pasted value in Hexadecimal, so it won't be the same number)
Now that you have found the "chain of numbers" inside the file, you modify the numbers you need... You save, and do it again with the second chain of numbers, save, and it should be ok.

But I strongly recommend using wxHexEditor, I found it a lot easier/convenient to use, because there is a "Find & Replace" tool which is pretty convenient (in the edit menu). Go on Edit->Replace, select Hex Mode, in "Search" field, you can directly past the value you want to replace/search(or type it by hand) but remove the spaces between the numbers ! In "Replace" field, same : put the value you want. Click on "Replace all". It should say "1 string replaced" (or something like that). Do the same with the second string you have to replace, save your file.

Once you understood how to manipulate the hex editor, it's in fact easy ! (it's always easy to do something when you know how to do it ;))
Hope this will work now ;)

Edit : I attached a screesnshot of the "Replace" window of wxHexEditor to show how it works exactly (the exemple is for having a resolution of 1280x720).
Value your want to replace :
580200006820030000
By the value :
D00200006800050000
You now have only to click on "Replace All". You should have confirmation that 1 string has been replaced.
After that, you'll have to look for the value 20030000C745F458020000 , and replace it by the value 00050000C745F4D0020000 (if I'm not mistaking in one number). Click on "Replace All", it should confim that 1 string has been modified. Save your file, and it should be ok to play in a 1280x720 resolution ! (just remember to put the in-game resolution to 800x600)

Edit2 : And if you play in another language than english, don't change the name of the modified .exe file : for me, it was making the game to launch in a window automatically if it wasn't the original "RCT.EXE" filename.