Cardano of Milan and Ferrari(His Student) solved the cubic and quartic equation.
View Cardano's Method
I find it way easier(other than using the cubic formula) to just use a simple algorithm to solve for the polynomial. Note that this approach only works when the cubic equation has an integer root. It is a result of (but not equivalent to) the rational root theorem.
For example, given a quintic equation.
Where are some integer.
To solve for , bring to the other side of the equation and factor out x.
This will yield,
Finding out the factors of (To 2 factors)
And substituting in the values into the equation.
Make sure both sides works for the equation. If so then you will find the solution.