Hi,
I have solved your equations for P,S,C, and N. You can verify for yourself that the following values
P -> 29.1392, S -> 6.85919, C -> -1.0852, N -> 12.8043 produce the correct result.
Since those variables mean the fertiliser component prices, their magnitude must not be negative.
(C is negative)
Please make sure you have provided correct equations.
Thank you,
Serge