7^x+7^(x-2)+7(x+1)=7*393

If the original problem were entered slightly incorrectly:

  7^x + 7^{(x - 2)} + 7^{(x + 1)}  =  7·393

7^x + 7^x · 7^-2 + 7^x · 7¹  =  7·393

(1 + 7^-2 + 7) · 7^x  =  7·393

(1 + 1/49 + 7) · 7^x  =  7·393

(393/49) · 7^x  =  7·393

 7^x  = (7·393)·(49/393)

 7^x  = 7·49 = 7³

x = 3

$${{\mathtt{7}}}^{{\mathtt{x}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{7}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right) = {\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{393}} \Rightarrow {\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\mathtt{50}}{\mathtt{\,\times\,}}{{\mathtt{7}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}{\mathtt{\,-\,}}{\mathtt{2\,744}}\right)}{{\mathtt{7}}}}$$

Easy one and difficulty:normal