0\; ,\; \; 2t^2-7t-4<0\\\\D=81\; ,\; t_1=\frac{7-9}{4}=-\frac{1}{2}<0\; ,\; \; t_2=\frac{7+9}{4}=4\\\\2(t+\frac{1}{2})(t-4)<0\qquad +++(-\frac{1}{2})--(0)--(4)+++\\\\t\in (0,4)\; \; \; \to \; \ \; 0<2^{-x}<4\\\\0<2^{-x}<2^2\ \; \; \to \\\\-x<2\\\\x>-2\\\\x\in (-2,+\infty )" alt="4^{-x+0,5}-7\cdot 2^{-x}-4<0\\\\(2^{-x})^2\cdot 2-7\cdot 2^{-x}-4<0\\\\t=2^{-x}>0\; ,\; \; 2t^2-7t-4<0\\\\D=81\; ,\; t_1=\frac{7-9}{4}=-\frac{1}{2}<0\; ,\; \; t_2=\frac{7+9}{4}=4\\\\2(t+\frac{1}{2})(t-4)<0\qquad +++(-\frac{1}{2})--(0)--(4)+++\\\\t\in (0,4)\; \; \; \to \; \ \; 0<2^{-x}<4\\\\0<2^{-x}<2^2\ \; \; \to \\\\-x<2\\\\x>-2\\\\x\in (-2,+\infty )" align="absmiddle" class="latex-formula">