Arguments for both sides began in October of 1977, and several justices found that they were split fiercely over the issue. By February of 1978, the case was still undecided. At that point, the votes were split four-to-three, with one justice, Justice Powell, left undecided. Those against the University of California's program were Chief Justice Warren Burger, William Rehnquist, John Paul Stevens, and Potter Stewart; those for the program were Thurgood Marshall - the leader of the advocates in the Court - William Brennan, and Byron White. Burger and the other critics were Marshall's major opponents, because not only were they against any kind of affirmative action, but they did not even wish to address the problem in this case; they wanted to focus only on whether Bakke should have been admitted to the university in the first place. Powell, the undecided justice, wanted to address the issue, but was uncertain as to whether that the University of California's program was unconstitutional. At the time, one of the other Supreme Court justices, Justice Blackmun, was recovering from surgery and had not cast his vote. .
Tension rose between the Justices until Blackmun finally spoke in May of 1978, coming down squarely on Marshall's side of the vote. In answer to Rehnquist's idea of an "abstract, rigid world," Blackmun said, "This is not an ideal world we live in a real world." (World) The final judgment of the Court was released in late June of 1978. Powell, the compromising justice assigned to issue the opinion in the case, agreed with the California Supreme Court that the University of California would be forced to admit Bakke, but said that the university should develop a "less intrusive" affirmative action program. .
Marshall released his own opinion on the case as well. He was outraged that the same Constitution that had previously allowed laws discriminating against blacks was being used to say that not all affirmative action, a correction for the previous injustices, was not legal.