Question 877951
The reason is because of that square root. If you had -9+21 over 6, then you can factor out 3. However, that 21 is buried in a root, so you can't factor out 3 from it. 


I guess you could say this


{{{-9+sqrt(21)=-9+sqrt(3*7)}}}


{{{-9+sqrt(21)=-9+sqrt(3)*sqrt(7)}}}


but that's about it and it's not a good step in terms of simplifying


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So I'd stick with the answers of 


{{{x = (-9+sqrt(21))/6}}} or {{{x = (-9-sqrt(21))/6}}}


you can condense them into one single equation


{{{x = (-9+-sqrt(21))/6}}}