[tex]\displaystyle\\
\log_{3}(x+2)=\log_3(x^2)\\
\text{Conditii:}\\
x+2 \ \textgreater \ 0~~~\Rightarrow ~~~ x\ \textgreater \ -2\\
x^2 \ \textgreater \ 0~~~\Rightarrow ~~~x\ \neq 0\\
==\Longrightarrow~~x\in (-2;~0)\bigcup(0;~+\infty)\\\\
\text{Avem egalitate intre doi logaritmi in aceeasi baza}\\\\
x+2=x^2\\\\
x^2-x-2=0\\\\
x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{1\pm\sqrt{1+4\cdot 2}}{2} =\frac{1\pm\sqrt{9}}{2}=\frac{1\pm3}{2}\\\\
x_1=\frac{1-3}{2}=\frac{-2}{2}=\boxed{-1}\\\\
x_2=\frac{1+3}{2}=\frac{4}{2}=\boxed{2}[/tex]