Quartic equation
Ferrari's solution
can be transformed into
satisfy
.Let us consider
Eliminating
and forming 
equations, we have:
,which reduces to the solution of a cubic equation.
Descarte's solution
Considering
with 
, the above can be transformed into
Factorizing the above results in:
satisfies
.Let
be a solution of the equation above. Then, we just need to solve the following equation:
Euler's solution
if we consider
, then 
is a solution of
.Expressing the solutions as
, the solutions of the quartic equation are:
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