[tex]\displaystyle\\
\log_{0,1}(x^2-x-1)=\log_{0,1}(x+4)\\\\
\text{Logaritmii au aceeasi baza.}\\\\
\Longrightarrow~~~(x^2-x-1)= (x+4)\\\\
x^2-x-1 -x-4 = 0\\\\
x^2-2x-5 = 0\\\\
x_{12}= \frac{-b\pm \sqrt{b^2-4ac} }{2a}=\frac{2\pm \sqrt{4+4\cdot 5} }{2}=\\\\
=\frac{2\pm \sqrt{24} }{2}= \frac{2\pm 2\sqrt{6} }{2}= 1\pm \sqrt{6}\\\\
\boxed{x_1 = 1-\sqrt{6}} \\\\
\boxed{x_2= 1+\sqrt{6}} [/tex]
