Quadratic Equations

How do I solve a quadratic equation?

There are different ways to solve a quadratic equation, the main ones that i'm thinking about right now are:

1) factor the equation as a product:

ex: x^2 + 4x + 3 = 0

(x+3) (x+1) = 0

x=-3 and x=-1 are the solutions.

To find (x+p) and (x+q) you have to think that (p+q) have to be equal to the number that is multiplied by x, in my example it was 4 (3+1=4), (p times q) have to be equal to the last number of the quadratic equation, the one that is not multiplied by any x, that in my example is 3 (3 x 1 = 3)

2) The other way to solve a quadratic function is by using a formula:

given: ax^2 + bx + c=0

x = (-b + / - √ (b^2 - 4ac)) / 2a

ex: 3x^2 + 4x - 2=0

x = (-4 + / - √16-4 (3) (-2)) / 6 = (-4 + / - √16+24) / 6 = (-4 + / - √40) / 6

now there are 2 possibilities: x = (-4 + √40) / 6

and

x = (-4 - √40) / 6

I hope the examples were clear enough also if i did't get very nice numbers. Look closely to the sings + and -, they are very important