$5 \times {\left( {8}^{2x} \right)}^{2}=-17 \times {8}^{2x}+12$
To get an equation that is easier to solve, substitute $t$ for ${8}^{2x}$$5{t}^{2}=-17t+12$
Solve the equation for $t$$\begin{array} { l }t=-4,\\t=\frac{ 3 }{ 5 }\end{array}$
Substitute back $t={8}^{2x}$$\begin{array} { l }{8}^{2x}=-4,\\{8}^{2x}=\frac{ 3 }{ 5 }\end{array}$
Solve the equation for $x$$\begin{array} { l }x\notin ℝ,\\{8}^{2x}=\frac{ 3 }{ 5 }\end{array}$
Solve the equation for $x$$\begin{array} { l }x\notin ℝ,\\x=\frac{ \ln\left({\frac{ 3 }{ 5 }}\right) }{ 6\ln\left({2}\right) }\end{array}$
Find the union$\begin{align*}&x=\frac{ \ln\left({\frac{ 3 }{ 5 }}\right) }{ 6\ln\left({2}\right) } \\&x\approx-0.122828\end{align*}$