solve 300=22t+1.2t^2

300=22t+1.2t^2    multiplying through by 10 to clear the decimal and rearranging, we have

12t² + 220t -3000 = 0      divide through by 4

3t² + 55t - 750 = 0          this can't be factored, so let's use the on-site calculator to solve it.....

$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{55}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{750}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{481}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{55}}\right)}{{\mathtt{6}}}}\\ {\mathtt{t}} = {\frac{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{481}}}}{\mathtt{\,-\,}}{\mathtt{55}}\right)}{{\mathtt{6}}}}\\ \end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = -{\mathtt{27.443\: \!093\: \!499\: \!551\: \!090\: \!7}}\\ {\mathtt{t}} = {\mathtt{9.109\: \!760\: \!166\: \!217\: \!757\: \!3}}\\ \end{array} \right\}$$

And there are the two solutions........