Question 293351
Your equation is:


{{{A/(((A/Y)+C+(700000/Y)-115000)*Y)=A/(C*X)}}}


Multiply both sides of this equation by {{{(((A/Y)+C+(700000/Y)-115000)*Y)}}} to get:


{{{A = (A * (((A/Y)+C+(700000/Y)-115000)*Y))/(C*X))}}}


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


{{{C*X = (((A/Y)+C+(700000/Y)-115000)*Y))}}}


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


{{{C*X = A + C*Y + 700000 - 115000*Y}}}


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


{{{C*X - A - 700000 = C*Y - 115000*Y}}}


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


{{{C*X - A - 700000 = Y*(C-115000)}}}


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


{{{(C*X - A - 700000)/(C-115000) = Y}}}


This is the same as:


{{{Y = (C*X - A - 700000)/(C-115000)}}}


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 = (C*X - A - 700000)/(C-115000)}}} becomes:


{{{Y = (10*15 - 5 - 700000)/(10-115000)}}} which becomes:


{{{Y = (150-5-700000)/(10-115000)}}} which becomes:


{{{Y = (-699855)/(-114990)}}} which becomes:


Y = 6.086224889


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


{{{A/(((A/Y)+C+(700000/Y)-115000)*Y)=A/(C*X)}}} becomes:


{{{5/(((5/6.086224889)+10+(700000/6.086224889)-115000)*6.086224889)=5/(10*15)}}} 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.