0\\5a^2-9a+4=0\\D=81-80=1\\a_1=\frac{4}{5};a_2=1\\(\frac{4}{5})^{x}=\frac{4}{5};(\frac{4}{5})^{x}=1\\x_1=1;x_2=0" alt="4*5^{2x}+5*4^{2x}=9*20^x (:5^{2x})\\ 4+ 5(\frac{4}{5})^{2x}=9(\frac{4}{5})^{x}\\(\frac{4}{5})^{x}=a;a>0\\5a^2-9a+4=0\\D=81-80=1\\a_1=\frac{4}{5};a_2=1\\(\frac{4}{5})^{x}=\frac{4}{5};(\frac{4}{5})^{x}=1\\x_1=1;x_2=0" align="absmiddle" class="latex-formula">