A hospital district as provided in section 39-1320 may be organized where it appears that said district will be within the boundaries of one (1) or more counties, where all the other requirements provided in section 39-1320 have been met, and the county commissioners of each county in which such district will be formed shall affirmatively find that the public welfare of that portion of the county will be served by the inclusion thereof in such joint county district, that such district is not an unnatural extension of a service district for hospital services, and that the petition for such district has been signed by not less than 10% of the qualified electors and taxpayers of that portion of the proposed district lying within the county.