Problem:
I want to display my search results to different page

Solution:
With view block you can chose different setting what you want to display, either search for, search results or both.

I've set the setting to display only search form and configured the search result page as you can see with the following screenshot:
=>https://nimb.ws/Twv5b8

And on your "Home Search Result" page I've added the view to display only search results:
=> https://nimb.ws/ANsjbD

You can find the proposed solution in this case with the following reply:
https://toolset.com/forums/topic/i-want-to-display-my-search-results-to-different-page/#post-2027195

Relevant Documentation: