No real solutions.....two "non-real".....
$${\mathtt{0.5}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{1}}{i}{\mathtt{\,-\,}}{\mathtt{3}}\\
{\mathtt{x}} = {i}{\mathtt{\,-\,}}{\mathtt{3}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,-\,}}{i}\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{i}\\
\end{array} \right\}$$
