What did the supreme court say in its ruling in regents of the university of california v. bakke (1978)?

Regents of the University of California v. Bakke (1978) upheld affirmative action, but struck down the use of racial quotas.

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The Supreme Court's decision gave some credence to Allan Bakke's claim that the University of California at Davis had practiced some amount of reverse discrimination in denying him admittance to the medical school because he was not an economically or educationally disadvantaged member of one of four racial/ethnic groups eligible for their special admission program.  But the Court was careful to note that race could be considered as a factor (among many factors) in college admissions, if  schools practiced great care in doing so.  Having a basic quota system, such as UC Davis reserving 16 spots out of 100 each year, was considered discriminatory.

The essence of the decision in Regents of the University of California v. Bakke was that the Court upheld affirmative action.  It allowed race to be considered as one of several factors in college admission policy.  But establishing specific racial quotas was an approach that the Court said was not allowable.