
Cubic Equations
I have a cubic equation that I need to find a real solution to, does anyone have any ideas??
The equation is ((A/B)1)*(((A/C)^2)1)=2*(A/C)*((D*E)/F)
where 1 is actually 1 and not the inverse. All values are known except for that of A, this is the value that I need to find.
Cheers,
Ben

Re: Cubic Equations
rearange so you have F(a)=0, multiplying through by any denominators. If the values are known, can't you use those instead of B,C,D,E,F

Re: Cubic Equations
Well the issue is that I'm rearranging the formula to use in a VBA program, so I need to input the variables as B,C,D,etc as the values are calculated earlier in the program. So I need an equation which solves A in terms of B,C,D,etc. I'm just having an absolute nightmare in reformulating it. Keep coming to dead ends.
(The value of F begins low and then increases until A is over a certain value)

Re: Cubic Equations
If those coefficients can be anything, then you will need the general "cubic" formula.
Let a and b be any two numbers.
Also, so subtracting, we have
If we let x= a+ b, m= 3ab, and , that equation is .
Now, the question is, if we know m and n, can we solve for a and b and so find x?
From m= 3ab, we get b= m/3a. Putting that into , we have . Multiply both sides by to get or which we can think of as a quadratic equation for .
By the quadratic formula, .
We can take that "2" in the denominator into the root and write
Because ,
That can be used to solve the "reduced cubic" with no " " term.
For the general cubic equation, , first let y= x+ q, for some unknown number q, so that
. Multiply that out and choose q so that the coefficient of is 0.