Thread: Rearranging the GEH Statistical Equation

Hi,

I use the GEH statistical equation in my line of work - traffic engineering.

The equation is as follows:



I would like to rearrange the equation such that "M"is on one side of the equation and GEH and "C" are on the other side of the equation. I am finding it very difficult to do.

Could anyone assist me with this please?

Thanks,

Toby

Hey tobyshadow.

We get:

GEH^2 = 2(M-C)^2/[M+C]
GEH^2*[M+C} = 2(M-C)^2
GEH^2*M + GEH^2*C = 2[M^2 - 2MC + C^2]
M[GEH^2 + 4C] = 2M^2 + 2C^2

M = [2M^2 + 2C^2]/[GEH^2 + 4C]
= 2M^2/[GEH^2 + 4C] + 2C^2/[GEH^2 + 4C]

Let a = 2/[GEH^2 + 4C] and c = 2C^2/[GEH^2 + 4C]

then we have the quadratic equation:

aM^2 - M + c = 0 which will have either no real solutions, one real solution, or two real solutions.

Depending on the context of the situation and on the C and GEH values, if you get two solutions you will probably eliminate one and get the right answer.

GEH^2 = 2(M-C)^2/[M+C]
GEH^2*[M+C} = 2(M-C)^2
GEH^2*M + GEH^2*C = 2[M^2 - 2MC + C^2]
M[GEH^2 + 4C] = 2M^2 + 2C^2

where did the GEH^2*C go?

Yeah I forgot it (thanks for spotting it). So it should be:

GEH^2*M + GEH^2*C = 2[M^2 - 2MC + C^2]
M[GEH^2 + 4C] = 2M^2 + 2C^2 - GEH^2*C

M = [2M^2 + 2C^2 - GEH^2*C]/[GEH^2 + 4C]
= 2M^2/[GEH^2 + 4C] + [2C^2 - GEH^2*C]/[GEH^2 + 4C]

Let a = 2/[GEH^2 + 4C] and c = [2C^2 - GEH^2*C]/[GEH^2 + 4C]

So aM^2 - M + c = 0 with new a and c.