What is the answer to -1000=5t(6.73-t)

-1000=5t(6.73-t)

 

$$\begin{array}{rll}
-1000&=&5t(6.73-t)\\
-200&=&t(6.73-t)\\
-200&=&6.73t-t^2\\
t^2-6.73t-200&=&0\\
t&=&\frac{6.73\pm\sqrt{6.73^2+4*1*200}}{2}

\end{array}$$

 

$${{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{6.73}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{200}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{8\,452\,929}}}}{\mathtt{\,-\,}}{\mathtt{673}}\right)}{{\mathtt{200}}}}\\
{\mathtt{t}} = {\frac{\left({\sqrt{{\mathtt{8\,452\,929}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{673}}\right)}{{\mathtt{200}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = -{\mathtt{11.171\: \!960\: \!652\: \!075\: \!797\: \!6}}\\
{\mathtt{t}} = {\mathtt{17.901\: \!960\: \!652\: \!075\: \!797\: \!6}}\\
\end{array} \right\}$$

-1000 = 5t(6.73 - t)

First we distribute 5t using the distributitive property:

-1000 = 5t(6.73) + 5t(t)

So we have:

-1000 = 33.65t + 5t

We can then add together the two t's:

-1000 = 38.65t

Now we divide both sides by 38.65 to fully isolate t:

-1000/38.65 = 38.65t/38.65

$${\mathtt{\,-\,}}{\frac{{\mathtt{1\,000}}}{{\mathtt{38.65}}}} = -{\mathtt{25.873\: \!221\: \!216\: \!041\: \!397\: \!2}}$$=t