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Quadratic equations are a type of algebra where x2 (x squared) is involved. There's a well-known formula for solving quadratic equations and I'll quote it here.
The usual form of a quadratic is:
And the equation is solved by:
There it is. A classic solution to a well-known mathematical problem. Many other explanations like this can be seen by going to a search engine and typing "Quadratic" or "Quadratic Equation". But at this site there are practical ideas which involve quadratic equations, for example the Video Tape Counter to Time. There's also a huge amount of other stuff, (see full site index) quite a lot of which isn't about mathematics, so I would guess there are better explanations elsewhere, but then again, looking around, I don't see any brilliant explanations. Maybe some recommendations could help to update this.
Depending on the numbers in the equation, a quadratic equation can have two solutions, just one solution, or no real solutions at all. In practical problems, it's usually possible to spot which solutions are sensible. For example a square lawn of area 16 square metres, the side is likely to be 4 metres long, rather than -4.