Алгебра, логарифмы, пожалуйста, помогите

0" alt="5*(\frac{5}{6})^{x-1} - 9*(\frac{6}{5} )^{x}+3=0\\\\5*\frac{6}{5}*(\frac{5}{6})^{x}-9*(\frac{6}{5})^{x}+3=0\\\\6*(\frac{5}{6})^{x} -9(\frac{6}{5})^{x}+3=0\\\\(\frac{5}{6} )^{x}=m,m>0" align="absmiddle" class="latex-formula">

$6m-\frac{9}{m}+3=0\\\\6m^{2}+3m-9=0\\\\2m^{2}+m-3=0\\\\D=1^{2} -4*2*(-3)=1+24=25=5^{2}\\\\m_{1}=\frac{-1+5}{4}=1\\\\m_{2}=\frac{-1-5}{4}=-1,5<0\\\\(\frac{5}{6})^{x}=1\\\\(\frac{5}{6})^{x} =(\frac{5}{6})^{0} \\\\x=0$