The mayor and city council shall meet as a board of equalization each year at such times as they shall determine to be necessary, giving notice of any such sitting at least ten days prior thereto by publication in a legal newspaper in or of general circulation in the city. When so assembled they shall have power to equalize all special assessments, not herein otherwise provided for, and to supply any omissions in the assessments and at such meeting the assessments shall be finally levied by them. A majority of all the members elected to the city council shall constitute a quorum for the transaction of any business properly brought before them, but a less number may adjourn from time to time and compel the attendance of absent members. When sitting as a board of equalization on special taxes, the city council may adopt such reasonable rules as to the manner of presenting complaints and applying for remedies and relief as shall seem just. It shall not invalidate or prejudice the proceedings of the board that a majority of the members thereof do not, after organization by a majority, continue present during the advertised hours of sitting so long as the city clerk or some member of the board shall be present to receive complaints and applications and give information. No final action shall be taken by the board except by a majority of all the members elected to the city council comprising the same, and in open session. All the special taxes herein authorized shall be levied and assessed on all lots, parts of lots, lands, and real estate to the extent of the special benefit to such lots, parts of lots, lands, and real estate, by reason of such improvement, such benefits to be determined by the city council sitting as a board of equalization, or as otherwise herein provided, after publication and notice to property owners herein provided. In cases where the city council sitting as a board of equalization shall find such benefits to be equal and uniform, such assessments may be according to the feet frontage and may be prorated and scaled back from the line of such improvement according to such rules as the board of equalization may consider fair and equitable and all such assessments and findings of benefits shall not be subject to review in any equitable or legal action except for fraud, injustice, or mistake.