Argument #1
The Court should rule in favor of Bakke.  The admissions practices of setting aside a fixed quota of seats in each class for minority members and considering race as a factor in determining whether to admit students violate the equal protection clause of the Fourteenth Amendment.

Argument #2
The Supreme Court should rule in favor of the Board of Regents (University of California at Davis).  Its admissions practices were designed to help ensure equal treatment of all people in the long run.  A person's race also indicates part of their heritage, which an admissions committee should be able to consider along with other factors in determining whether or not to admit a student.