DETROIT — Michigan’s ban on affirmative action in college admissions was declared unconstitutional Thursday by a deeply divided federal appeals court, six years after state voters said race could not be an issue in choosing students.

In an 8-to-7 decision, the court said the 2006 amendment to the Michigan Constitution is illegal because it presents an extraordinary burden to opponents who would have to mount their own long, expensive campaign through the ballot box to protect affirmative action.