h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

For people who have no idea about mathematics it might be a good idea to link to an entry about the basics of algebra (I'm assuming there is one, if not maybe one should be written).

I know a bit about algebra so I followed most of it, but I got a bit lost when it got to putting the numbers into the formula. Where did the 7 go? where did the 5 come from? I take it this is a mistake and the original formula should have been 3x2+5x-42=0?

It may help to explain how you decide what numbers to substitute for a, b and c. for instance, if the formula was 3x3+5x-42=0 would the 3 still be a or would you need a "cubed quadratic formula" or something?

Just a bit of clarification for the dummies like myself.

The a is the number in front of the x-squared, the b is the number in front of the x and the c is the number on its own. That's always the case, even when one of the numbers = zero.
The quadratic formula, alas, does not work for cubic equations. You have to use someting called the Factor Theorum, which I won't go into because it's horribly complicated.