solving for i, on a parabola

[madifier]

I stumbled across an equation that I have been working with for a long time now. I'm hoping I'm correct that this is an algebra problem, but statistically speaking I'm wrong most of the time.

s*e + i*e + i^2 - a*(s+i) == 0

I would like to solve for 'i', but I don't even know if that's going to be possible or not. I've had math professors do some pretty crazy stuff which was awesome, but way out of my league.
In my spreadsheet I've plugged all sorts of numbers in for 'i' in an attempt to study how the equation works, and I receive back unique answers leading me to believe that it should be possible to solve for 'i'.
I've gotten to the point of just shifting variables around just for jollies to see if that would help, but alas no sparks of brainstorming occurred.
i^2 + (s+i)*(e-a) == 0
(e-a) == -( i^2 / (i+s) )

It's been a few years since I've been in the classroom, so my skills are rusty to say the least. However this problem has been haunting me regardless.
This equation is part of a bigger problem, so if this doesn't have a solution then that's okay. I'll just have to attack it from a different angle.
Worst case scenario I can plug numbers in for everything else and have the computer close in on a precise point much like a bezier curve.

The bigger problem is associated with a parabola, so there are two possible points that the parabola passes at the x-axis.
'i' does not represent two different points, but rather the distance from 's' where 's' is the center of the parabola. Much like a circle with a radius ( center point, distance to edge )

Thank you for your time.

 

[lookagain]

s*e + i*e + i^2 - a*(s+i) == 0

I would like to solve for 'i', but I don't even know if that's going to be possible or not. .

I don't know if you have the correct equation at the outset. Also, I will not
assume that e here is the constant that is approximately equal to 2.71828,
because I know that in certain contexts of certain problems that e is used
for the value of the eccentricity, just for one example.

I will assume that s, e, and a are variable constants.

es + ei + i^2 - a(s + i) = 0


This is quadratic in the variable i.


es + ei + i^2 - as - ai = 0

i^2 + ei - ai + es - as = 0

i^2 + (e - a)i + (es - as) = 0


This is in the form Ai^2 + Bi + C = 0

You may use the Quadratic Formula on it.
(Look it up if you don't already have it memorized.)

A = 1

B = (e - a)

C = (es - as)


If you substitute these values into the formula, initially you will have


\(\displaystyle i \ = \ \dfrac{-(e - a) \pm \sqrt{(e - a)^2 - 4(1)(es - as)}}{2(1)}\)



madifier,

can you work further with this?

 

[madifier]

I hadn't considered the quadratic formula, I will try to play with that. Thanks.

I can't believe I forgot to declare them earlier, good grief. Maybe I'm the one who needs to be debugged.

es + ei + i^2 - a(s + i) = 0

The puzzle I have starts with 's',
thus determines what 'e' should be,
then the user makes a decision what step along the path he wants ('a' = {1,2,3,4,5,...})
and finally 'i' is the distance between steps, which is crucial information.

's' is a precalculated const
'e' is a const based off of 's'
'a' is also a const which is user defined, much like f(x) = x.
'i' is the unknown value I'm looking for.

I call it a puzzle because I stumbled across it myself and haven't been very successful at finding information on it. Kind of hard to google something that has no name. It probably is out there and I'm overlooking it.