Resolving this recurrence equation
Construct a recursion tree. The sum of the costs per level is less then $c\cdot n$, for $c$ being the constant in the $O(n)$. The tree has roughly $n\log_4 n$ full levels, and the deepest level is $n \log_{4/3} n$. So, summing up over all levels gives $T(n)=O(n\log n)$.