> OK, so "everybody knows" (?!) that ax^2 + bx + c = 0 can be transformed 
> into the magical expression
>
>   x = (-b +/- Sqrt(b^2 - 4ac)) / 2a
>
> But why is that, exactly? Well, looking in my sister's A-level maths book 
> [unlike me, my sister was *taught* mathematics] I discover a long sequence 
> of algebraic manipulations that slowly transforms the one into the other.

It's not that hard or long, just involves dividing by a, completing the 
square for the first two terms, rearranging, taking the square root, and 
rearranging again for x.

But I imagine the cubic is a lot harder.

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