Solve a recurrence by drawing the recursion tree?
Use the Akra-Bazzi method. In terms of the notation there you have:
$$
\begin{align*}
g(x) &amp;= \frac{x}{2} = O(x^c) \\
a_i  &amp;&gt; 0 \quad \forall i \\
0 &amp;&lt; b_i &lt; 1 \quad \forall i \\
\end{align*}
$$
The requisites check out (and the somehow implied differences $h_i(x)$  due to truncation if the divisions don't come out exact also check out). So we need the $p$ for which:
$$
\left( \frac{1}{5} \right)^p + \left( \frac{4}{5} \right)^p = 1
$$
which is seen to be $p = 1$. Plugging into the equation:
$$
T(x) = \Theta \left( x^p \left( 1 + \int_1^x \frac{g(u) d u}{u^{p + 1}} \right) \right)
     = \Theta (x (1 + \frac{1}{2} \ln x))
     = \Theta (x \ln x)
$$