If there be no remonstrance, or if the finding be in favor of the validity of the proceedings or after the report shall have been modified to conform to the findings, the court shall confirm the report and order of confirmation shall be final and conclusive, the proposed work shall be established and authorized and the proposed assessments approved and confirmed, which approval and confirmation shall be final, unless within thirty days an appeal be taken to the supreme court.
NMS § 73-7-9