I assume this is taken from physics textbook or so. In particular, I assume $m$ (for mass), $\omega$ (angular frequency?), as well as $\sigma_x$ and $\sigma_p$ (standard deviation terms) to be positive. The symbols are now defined.
Then the The given inequality follows by applying the AM-GM inequality to the nonnegative quantities $\frac{\sigma_p^2}{m}$ and $m \omega^2 \sigma_x^2$: $ \frac{1}{2} \left( \frac{\sigma_p^2}{m} + m \omega^2 \sigma_x^2 \right) \geq \sqrt{\frac{\sigma_p^2}{m} \times m \omega^2 \sigma_x^2} = \omega \sigma_p \sigma_x. $
Alternatively, you can also deduce this by expanding: $ \frac{1}{2} \left( \frac{\sigma_p}{\sqrt{m}} - \sqrt{m} \cdot \omega \sigma_x \right)^2 \geq 0. $
The two other terms involving $\mathrm{E}(x)^2$ and $\mathrm{E}(p)^2$ are nonnegative, so they do can be safely added to left hand side of the inequality.