Dror Bar-Natan: Classes: 2003-04: Math 157 - Analysis I:

Monsters

Web version: http://www.math.toronto.edu/~drorbn/classes/0304/157AnalysisI/Monsters/Monsters.html

The linear equation and a tame formula:

Solve[a x + b  == 0,  x]

The quadratic equation and the monster:

Solve[a x^2 + b x + c == 0,  x]  //  First

The cubic equation and the horrible monster:

Solve[a x^3 + b x^2 + c x  + d == 0, x]  //  
      First

The quartic equation and the truly horrible monster:

Solve[a x^4 + b x^3 + c x^2  + d x  +  e == 0, x]  //  
      First

The quintic equation; we're dead now:

Solve[
        a x^5 + b x^4 + c x^3  + d x^2  +  e x  +  f == 0, 
        x]  //  First