Need help with solving an equation that has the variable in the equation twice

brikenmcc 

Let's say Max Capacity is in A2, Setup Time in B2 and Time per Unit in C2. We want Batch Size in D2.

The equation can be written as:

A2 = D2/(B2+D2*C2)

Multiply both sides with (B2+D2*C2):

A2*(B2+D2*C2) = D2

Evaluate the expression on the left:

A2*B2+A2*D2*C2 = D2

Subtract A2*D2*C2 from both sides:

A2*B2=D2-A2*D2*C2

Factor out D2 on the right hand side:

A2*B2 = D2*(1-A2*C2)

Divide both sides by (1-A2*C2):

A2*B2/(1-A2*C2) = D2

And there we have our formula for D2 (i.e. X):

=A2*B2/(1-A2*C2)

Enter the parameters in A2, B2 and C2 and D2 will show the Batch Size needed.

You may want to round up or down to a whole number by wrapping the above expression in ROUND.