Like Idran said before, it's just the quadratic formula. We had this DRILLED into us by our eighth grade algebra teacher, and it's come in handy.
Here's the low down:
You have this.
12x^2 - 6x + 21 = 0
The quadratic formula is:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
Now, here's where we plug numbers in. Your major variables will be a, b, and c. Using these, we get (usually) two values for x. Here's how to get find the variables.
A is the number that you multiply x^2 by. In this case,
12x^2, it's 12. Often you'll find that there is no multiplier, in which case, you have 1, because 1x^2 is the same as x^2.
B is the number that you multiply your second x by. So,
-6x makes this number -6.
C is the last number in the equation. +21.
So now we have a = 12, b = -6, and c = 21. Let's plug these in, shall we?
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
x = (-[-6] +/- sqrt([-6]^2 - 4[12][21])) / 2[12]
x = (6 +/- sqrt(36 - 1008)) / 24
x = (6 +/-
sqrt(-972)) / 24
Notice the sqrt(-972)? We can't take a square root of a negative number, so the problem is unsolvable in the real number system. We can use
i to represent non-real numbers, but that's a whole new can of worms. Suffice it to say, this problem's answer cannot be expressed in real numbers. As Idran also said, the discriminant (b^2 - 4ac) will be positive to get two answers, zero for one answer, or negative for a non-real answer. In this case, our discriminant is negative.
This ends my lesson on the quadratic formula, and I hope my elaboration helped you. You can use this formula on ANY equation that follows the pattern of x^2 + x + 1 = 0 or something to that effect. With more experience you'll be able to pick these out and work with them, no problem. I hope I didn't just confuse the hell out of you or say something wrong.
EDIT: I also hope I'm not acting condescending towards you - that's not my intention. It just seemed like you needed elaboration on Idran's advice.
EDIT Mk II: The asnwers are (hopefully):
(6 + 31.177
i) / 24 and (6 - 31.177
i) /24
Please, someone call me on this stuff if I'm wrong. It behooves me to know it as well. <p>
Remember, pillage first, THEN burn.
A waist is a terrible thing to mind.
Eat well, stay fit, die anyway.</p>
Edited by: [url=http://pub30.ezboard.com/brpgww60462.showUserPublicProfile?gid=rhelianalto>Rhelian] at: 8/24/03 2:32 am