Master Theorem Usage
You can use the idea of the Master Theorem and apply it to these occurrences. That is what I have done here, I would recommend looking at that answer because it will answer your question.

Basically we can look at the fractional terms inside the recurrence calls. If the sum to less than $n$, then the "conquer" part of "divide-and-conquer" will dominate the "divide" part. 

For your example we have the fractions: $\frac{n}{5} + \frac{7n}{10} = \frac{9n}{10} &lt; n$. Therefore the $O(n)$ term will dominate and the overall time complexity will be $\Theta(n)$. This is an idea of the Master Theorem, figuring out which dominates: "divide" or "conquer". Again, I highly suggest looking at this answer for a more in-depth proof.