Here is a solution with {NiceArray} of nicematrix.

\documentclass{article}
\usepackage{nicematrix}

\begin{document}

\[  
\renewcommand{\arraystretch}{2}
\begin{NiceArray}{|c|ccccccccccccc|c|}[hlines]
    x & -\infty & & & -1 & & & 0 & & & 1 & & & +\infty & 
     \Block{2-1}{\mathbf{Separarea} \\ \mathbf{soluțiilor}} \\ 
    \diagbox{\textbf{m}}{f(x)} & -\infty & & & -m + \ln 2 - \frac{1}{2} & & & -m & & & -m + \ln 2 - \frac{1}{2} & & & -\infty & \\ 
    m \in (-\infty, -1)
     & - & & & + & & & + & & & + & & & - & 
    \Block{}{ x_1 \in (-\infty, -1) \\ x_2 \in (1, \infty)} \\
\end{NiceArray}
\]

\end{document}

You need several compilations (because nicematrix uses PGF/TikZ nodes under the hood).