quadratics

OK.......we're using the quad formula to find the solutions.

First....let's write out the quad formula........we have:

[-b ± √(b² - 4ac)] /  [2a]  where.... a = 3    b = 4  c = -2     ....  so we have

[-4 ± √(4² - 4(3)(-2))] /  [2(3)]  =

[-4 ± √(16 + 24)] /  [6)]  =

[-4 ± √(40)] /  [6)] =

[-4 ± √(10)*4] /  [6)] =

[-4 ± 2√(10)] /  [6)]         Now....divide the "-4"  the "2" and the "6" all by 2......this gives us

[-2 ± √(10)] /  [3)]           And that's the answer as shown by the on-site solver. It also gives us the decimal approximations for both solutions!!!!

$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{10}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}{{\mathtt{3}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{10}}}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}{{\mathtt{3}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{1.720\: \!759\: \!220\: \!056\: \!126\: \!4}}\\
{\mathtt{x}} = {\mathtt{0.387\: \!425\: \!886\: \!722\: \!793\: \!1}}\\
\end{array} \right\}$$

thanks a bunch!