Within a city of the metropolitan class, in case the lots and real estate abutting upon that part of the street ordered paved as shown upon any plat or map are not of uniform depth, as well as in all cases where, in the discretion of the city council sitting as a board of equalization, it is just and proper so to do, such board shall have the right and authority to fix and determine the depth to which the real estate shall be charged and assessed with the cost of such improvement, without regard to the line of such lots. Such assessments shall be fixed and determined upon the basis of benefits accruing to the real estate by reason of such improvement. The provisions of this section, in regard to the depth to which real estate may be charged and assessed, shall apply to all special assessments.