$$4\cdot2^{2x+1}-9\cdot2^{x}+1=0; 4.2^{2x+1}-9\cdot2^{x}+1=0; 4.2^{2x}\cdot2^{1}-9\cdot2^{x}+1=0$$
$x=\frac{i\times 2\pi n_{1}}{\ln(2)}\text{, }n_{1}\in \mathrm{Z}\text{, }\frac{21\times 17.64^{\frac{2\pi n_{1}i}{\ln(2)}}}{5}-9\times 2^{\frac{2\pi n_{1}i}{\ln(2)}}+1=0\text{ and }2\times 17.64^{\frac{2\pi n_{1}i}{\ln(2)}}-9\times 2^{\frac{2\pi n_{1}i}{\ln(2)}}+1=0$
$x=\frac{i\times 2\pi n_{2}}{\ln(2)}-3\text{, }n_{2}\in \mathrm{Z}\text{, }\frac{21\times 17.64^{\frac{2\pi n_{2}i}{\ln(2)}-3}}{5}-9\times 2^{\frac{2\pi n_{2}i}{\ln(2)}-3}+1=0\text{ and }2\times 17.64^{\frac{2\pi n_{2}i}{\ln(2)}-3}-9\times 2^{\frac{2\pi n_{2}i}{\ln(2)}-3}+1=0$