First you need a boring digression into determinants. Not only can one covert an equation into a determinants, it is possible to convert a determinants into an equation (the technical term is "expansion"). When one has finished converting a determinants into Basic Nomographic Form, one should convert the determinants into an equation and ensure that it matches your original equation. Just to be sure you didn't make a slight mistake along the line.

Here is a determinant of the second order:

To expand it, one cross multiplies the elements, and subtracts the results. The determinant expands to (A₁B₂) - (A₂B₁)

Here is a determinant of the third order:

To expand it, one first has to convert it into an expression composed of 2^nd order matrices:

If you don't care how this was done, just skip the rest of this paragraph. The first 2^nd order determinant was made by suppressing the first row and column of the original 3^rd order determinant. The second 2^nd order determinant is by suppressing the first row and second column and the third 2^nd order determinant is by suppressing the first row and third column.

To complete the expansion, expand each 2^nd order determinant. The final result is:

which reduces to:

Armed with this knowledge you can now tackle the intricate task of actual insertion.