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$- \frac{27}{4}+( \frac{2}{3} )^{2x}+2^{x-2}*3^{1-x}=0\\\\( \frac{2}{3})^{2x}+ \frac{2^x}{2^2}* \frac{3}{3^x}- \frac{27}{4}=0\\\\( \frac{2}{3})^{2x}+ \frac{3}{4}* (\frac{2}{3})^x- \frac{27}{4}=0\\\\a=( \frac{2}{3})^x\\\\a^{2x}- \frac{3}{4}a^x- \frac{27}{4}=0\\\\D=( \frac{3}{4})^2-4*1*(- \frac{27}{4})= \frac{9}{16}+27= \frac{441}{16}=( \frac{21}{4})^2\\\\a_1= \frac{- \frac{3}{4}+ \frac{21}{4} }{2}= \frac{9}{4}\\\\a_2=a_1= \frac{- \frac{3}{4}- \frac{21}{4} }{2}=-3\; \; (\ \textless \ 0)$

$( \frac{2}{3})^x= \frac{9}{4}\\\\( \frac{2}{3})^x=( \frac{2}{3})^{-2}\\\\x=-2$