More solving quadratic equations: the quadratic formula again, what we've all been waiting for. the quadratic formula is pretty easy to remember, and will always work, even if the solutions to the quadratic equation aren't always real numbers (they can be imaginary - the square roots of negative numbers). so here it is: x = -b ± √b2 - 4ac 2a

You don't have a question in there but I can tell you that the quadratic formula that is shown is not quite correct.
x = -b ± √b2 - 4ac 2a
For one thing, the first 3 terms should ALL be divided by 2a
The square root symbol should be extended from b^2 through 4ac
The division symbol is missing.
So the quadratic formula SHOULD read:
x = [-b +- sq root (b^2 - 4ac) ] / 2a
Also I have attached a graphic of the quadratic formula.