\[f(x) = 0\]
\[\frac{1}{2}x^{2} + 3x = 0\]
\[x\left( \frac{1}{2}x + 3 \right) = 0\]
\[x = 0\ \ \ \ \ \ \ \ \ \frac{1}{2}x = - 3\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 6.\]
\[f(x) = 0\ \Longrightarrow при\ x = 0;\ \ x = - 6.\]