Although there is a method for cubics, there are no simple analytical ways.
Sometimes you may be able to use the remainder theorem to find one solutions. THen you can divide the original equation using that solution so that you are now searching for an equation of a lower order. If you started off with a cubic you will now have a quadratic and, if all else fails, you can use the quadratic formula.
You could use a graphic method. A cubic musthave a solution although that solution need not be rational. A quartic need no have any.
Lastly, you could use a numeric method, such as the Newton-Raphson iteration.
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I looked all over the internet and could not find a parametric equation for this shape. You can look at the link below to find the regular cartesian equation. If you are good at parametric equations you could probably convert this into parametric form. I am not so good at parametric equations.
if you can, you could always search a online calculator and use that.
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
Cramer's Rule is a method for using Matrix manipulation to find solutions to sets of Linear equations.
You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.