$7.9 \quad 3 \cdot 5^{2x-1}-2 \cdot 5^{x-1}=0.2$.

Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly. 

$7.9 \quad 3 \cdot 5^{2x-1}-2 \cdot 5^{x-1}=0.2$.
7.9 We have $5^{2 x-1}=5^{2 x} \cdot 5^{-1} ; 5^{x-1}=5^{x} \cdot 5^{-1} ; 0.2=5^{-1}$. After dividing all terms of the given equation by $5^{-1}$, it will take the form

$3 \cdot 5^{2 x}-2 \cdot 5^{x}=1$.

Let $5^{x}=y$, where $y>0$. Then we get the equation $3 y^{2}-2 y-1=0$, from which $y_{1}=1, y_{2}=-\frac{1}{3}$ (does not fit because the condition $y>0$ is not met). Therefore, $y=1$, from which $\boldsymbol{x}=\mathbf{0}$.

Answer: $x=0$.