What are the methods for solving a 3rd degree equation?

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To solve a third-degree equation of the form x^3 - ax^2 + bx + c = 0, various methods are available. The cubic formula can be used to derive the roots, and resources like Mathworld provide detailed explanations on this topic. For those looking for numerical solutions, online solvers can simplify the process. Understanding the complexity of cubic equations is essential for finding accurate solutions. Utilizing these methods can effectively lead to the determination of the variable x.
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i have a 3rd degree equation as follows. how can i solve this. What are the methods available?

x^3-a*x^2+b*x+c=0

i want to find x. a,b,c are all constants
 
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The solution is less than simple, but you can use the cubic equation so get it.
 
The solution to this was already given :

https://www.physicsforums.com/showthread.php?t=71782 [/URL]
 
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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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