how do i solve this

97a^3+0.564a=0  ....  factoring, we have

a(97a^2 + .564) = 0     the only real solution is a = 0

Note substituting x for a and using the on-site solver, we have

97x^2 + .564 = 0

$${\mathtt{97}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.564}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{141}}}}{\mathtt{\,\times\,}}{i}}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{970}}}}\right)}}\\
{\mathtt{x}} = {\frac{{\sqrt{{\mathtt{141}}}}{\mathtt{\,\times\,}}{i}}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{970}}}}\right)}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{0.076\: \!252\: \!429\: \!401\: \!893\: \!3}}{i}\\
{\mathtt{x}} = {\mathtt{0.076\: \!252\: \!429\: \!401\: \!893\: \!3}}{i}\\
\end{array} \right\}$$