What was the supreme court’s rationale for its plessy v. ferguson decision? what impact did the decision have on the north? the south?

Back then the supreme court ruled that racially separate facilities, if equal, did not violate the Constitution. 
This indicates that racial segregation itself is regarded as legal by the Supreme court. Because of this, many people in the south started to separate their establishment and creating racial discrimination in the society.
Even though there is a couple occurrence while the north tried to do discriminate minorities, the majority of people tend to despise this ruling and keep creating effort to override it.