34.8 = 10.9 *t + 4.9t^2

34.8 = 10.9 *t + 4.9t^2   let's mulftiply throgh by 10 to clear the decimals

348 = 109t + 49t^2   rearrange

49t^2 + 109t - 348 = 0

Using the onsite solver, we have

$${\mathtt{49}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{109}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{348}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\frac{{\mathtt{87}}}{{\mathtt{49}}}}\\
{\mathtt{t}} = -{\mathtt{4}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{1.775\: \!510\: \!204\: \!081\: \!632\: \!7}}\\
{\mathtt{t}} = -{\mathtt{4}}\\
\end{array} \right\}$$