SOLUTION: I need help solving the following equation for Y: {{{A/(((A/Y)+C+(700000/Y)-115000)*Y)=A/CX}}}

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Question 293351: I need help solving the following equation for Y:
A%2F%28%28%28A%2FY%29%2BC%2B%28700000%2FY%29-115000%29%2AY%29=A%2FCX
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Your equation is:

A%2F%28%28%28A%2FY%29%2BC%2B%28700000%2FY%29-115000%29%2AY%29=A%2F%28C%2AX%29

Multiply both sides of this equation by %28%28%28A%2FY%29%2BC%2B%28700000%2FY%29-115000%29%2AY%29 to get:

A+=+%28A+%2A+%28%28%28A%2FY%29%2BC%2B%28700000%2FY%29-115000%29%2AY%29%29%2F%28C%2AX%29%29

Multiply both sides of this equation by C*X and divide both sides of this equation by A to get:

C%2AX+=+%28%28%28A%2FY%29%2BC%2B%28700000%2FY%29-115000%29%2AY%29%29

Simplify by multiplying the right side of the equation by the factor of Y to remove the parentheses to get:

C%2AX+=+A+%2B+C%2AY+%2B+700000+-+115000%2AY

Subtract A and subtract 700000 from both sides of this equation to get:

C%2AX+-+A+-+700000+=+C%2AY+-+115000%2AY

Factor out the Y from the right side of the equation to get:

C%2AX+-+A+-+700000+=+Y%2A%28C-115000%29

Divide both sides of this equation by (C-115000) to get:

%28C%2AX+-+A+-+700000%29%2F%28C-115000%29+=+Y

This is the same as:

Y+=+%28C%2AX+-+A+-+700000%29%2F%28C-115000%29

If we did this correctly, your original equation and your final equation should yield the same answer.

I tested by letting A = 5, C = 10, X = 15.

I plugged those values into the final equation as follows:

Y+=+%28C%2AX+-+A+-+700000%29%2F%28C-115000%29 becomes:

Y+=+%2810%2A15+-+5+-+700000%29%2F%2810-115000%29 which becomes:

Y+=+%28150-5-700000%29%2F%2810-115000%29 which becomes:

Y+=+%28-699855%29%2F%28-114990%29 which becomes:

Y = 6.086224889

I then plugged all these values into the original equation to see if it was true.

A%2F%28%28%28A%2FY%29%2BC%2B%28700000%2FY%29-115000%29%2AY%29=A%2F%28C%2AX%29 becomes:

which becomes:

.033333334 = .033333333 which is true confirming that the translation of the equation by solving for Y is good.

There's a slight error factor that's probably due to rounding.

I'd be surprised if it's anything other than that.