[tex]2^{2x+1}+2^{x+2}=160\\
2^{2x}\cdot 2+2^{x}\cdot 4=160|: 2\\
(2^x)^2+2^{x}\cdot 2=80\\
(2^x)^2+2\cdot 2^{x}-80=0\\
Not.2^x=t,t\ \textgreater \ 0\\
t^2+2t-80=0\\
\Delta=4+4\cdot 80=324\Rightarrow \sqrt{\Delta}=18\\
t_1=\dfrac{-2+18}{2}=8\\
t_2=\dfrac{-2-18}{2}=-10\ \textless \ 0\\
2^x=8\Rightarrow \boxed{x=3(\text{solutie unica)}}[/tex]
