+118723 $${\mathtt{16}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{105}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,\small\textbf+\,}}{\mathtt{34}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{8\,849}}}}{\mathtt{\,-\,}}{\mathtt{105}}\right)}{{\mathtt{32}}}}\\
{\mathtt{t}} = {\frac{\left({\sqrt{{\mathtt{8\,849}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{105}}\right)}{{\mathtt{32}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{0.341\: \!589\: \!889\: \!970\: \!270\: \!7}}\\
{\mathtt{t}} = {\mathtt{6.220\: \!910\: \!110\: \!029\: \!729\: \!3}}\\
\end{array} \right\}$$
If you want to do it by hand use the quadratic formula
a=16, b=-105 and c=34
If you do not know the quadratic formula, here it is.
+118723 $${\mathtt{16}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{105}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,\small\textbf+\,}}{\mathtt{34}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{8\,849}}}}{\mathtt{\,-\,}}{\mathtt{105}}\right)}{{\mathtt{32}}}}\\
{\mathtt{t}} = {\frac{\left({\sqrt{{\mathtt{8\,849}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{105}}\right)}{{\mathtt{32}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{0.341\: \!589\: \!889\: \!970\: \!270\: \!7}}\\
{\mathtt{t}} = {\mathtt{6.220\: \!910\: \!110\: \!029\: \!729\: \!3}}\\
\end{array} \right\}$$
If you want to do it by hand use the quadratic formula
a=16, b=-105 and c=34
If you do not know the quadratic formula, here it is.
