Calculus implicit differentiation problem?

Question

S-5PW=3QW^2-6PQ 

What value of W minimizes S? P and Q are positive constants. 

Answer 1

The equation is  S - 5 PW = 3QW^ 2 - 6PQ

 S = 5PW+3QW^2 - 6PQ

To find the maximum or minimum value  dS / dW = 0

That is dS/dW = 6QW +5P

Now dS/dW = 0

6QW + 5P = 0

6QW =-5P

W = - 5P / 6Q

Hence W = - 5P / 6Q  minimizes S.