183k^3 + 61k - 3 = 0 How to solve this?

Desmos is for graphing not for solving.  So there is no mystery about that :))

It does not have nice integer solutions so I would use Desmos or Wolfram|Alpha to solve it

http://www.wolframalpha.com/input/?i=183k^3%20%2B%2061k%20-%203%20%3D%200

If I needed to do it myself I would use Newton's method of approximating roots

183k^3 + 61k - 3 = 0

The onsite solver will do this, too......the answer is pretty nasty...!!!

$${\mathtt{183}}{\mathtt{\,\times\,}}{{\mathtt{k}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{61}}{\mathtt{\,\times\,}}{\mathtt{k}}{\mathtt{\,-\,}}{\mathtt{3}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{k}} = {\left({\frac{{\sqrt{{\mathtt{15\,613}}}}}{{\mathtt{3\,294}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{122}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}\left({\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,-\,}}{\frac{\left({\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}{\left({\mathtt{9}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{15\,613}}}}}{{\mathtt{3\,294}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{122}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}\\
{\mathtt{k}} = {\left({\frac{{\sqrt{{\mathtt{15\,613}}}}}{{\mathtt{3\,294}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{122}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}\left({\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,-\,}}{\frac{\left({\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}{\left({\mathtt{9}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{15\,613}}}}}{{\mathtt{3\,294}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{122}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}\\
{\mathtt{k}} = {\left({\frac{{\sqrt{{\mathtt{15\,613}}}}}{{\mathtt{3\,294}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{122}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{\left({\mathtt{9}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{15\,613}}}}}{{\mathtt{3\,294}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{122}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{k}} = {\mathtt{\,-\,}}{\mathtt{0.024\: \!415\: \!509\: \!892\: \!177\: \!8}}{\mathtt{\,-\,}}{\mathtt{0.578\: \!896\: \!955\: \!168\: \!551\: \!4}}{i}\\
{\mathtt{k}} = {\mathtt{\,-\,}}{\mathtt{0.024\: \!415\: \!509\: \!892\: \!177\: \!8}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.578\: \!896\: \!955\: \!168\: \!551\: \!4}}{i}\\
{\mathtt{k}} = {\mathtt{0.048\: \!831\: \!019\: \!784\: \!355\: \!5}}\\
\end{array} \right\}$$

Thanks Chris,

I often forget how clever our own site calculator is. 

Thank you Mr Massow for making it for us.  

Note....Desmos is rather funky about solving these equations....

It will not "solve"  183x^3 + 61x - 3 = 0

It will "solve"   183x^3  =  3 - 61x   if the left and right sides are entered as separate functions .....

See this......https://www.desmos.com/calculator/se02owjof1

Go figure....!!!