> For the complete documentation index, see [llms.txt](https://jona-projects.gitbook.io/kiwicalc/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jona-projects.gitbook.io/kiwicalc/equations/quintic-equations-and-above.md).

# Quintic equations and above

#### According to Abel's impossibility theorem, a general formula for solving equations of degree 5 or higher does not exist. Therefore, in order to solve such equations, we can use use numerical methods. These methods are iterative - they generate closer approximations to the solutions on each iteration, so after a certain number of iterations the approximations converge to the solutions. Hopefully this general explanation of numerical root-finding methods was clear enough for you to understand. If not, that's ok, since you don't have to know how the library works in order to use it

You can solve these kind of equations with the numerical root-finding methods which were implemented in the library, so I recommend you look at the [numerical methods](broken://pages/pTRMHHLCs8F75wD3kRE1) section of this documentation. In short, if you wish to find only 1 root, you can use the [newton\_raphson()](broken://pages/pTRMHHLCs8F75wD3kRE1) and its counterparts, but if you wish to find all of the roots, you can use the [durand\_kerner()](broken://pages/pTRMHHLCs8F75wD3kRE1) method or the [aberth\_method()](broken://pages/pTRMHHLCs8F75wD3kRE1) method   

You can read more on that on the numerical method section of this docs.