0\\\2t^2-3t-2=0\\D=9+4\cdot(-2)=9-8=1\\t_{1,2}=\frac{3\pm1}4\\t_1=\frac12\\t_2=1\\\\2^x=\frac12\\2^x=2^{-1}\\x_1=-1\\\\2^x=1\\2^x=2^0\\x_2=0" alt="2\cdot2^{2x}-3\cdot2^x-2=0\\2^x=t,\;2^{2x}=t^2,\;t>0\\\2t^2-3t-2=0\\D=9+4\cdot(-2)=9-8=1\\t_{1,2}=\frac{3\pm1}4\\t_1=\frac12\\t_2=1\\\\2^x=\frac12\\2^x=2^{-1}\\x_1=-1\\\\2^x=1\\2^x=2^0\\x_2=0" align="absmiddle" class="latex-formula">