Another method

S=S(x)

Obiviously,the soltion must less than zero.

let x=-1, get 2a+b
Let x=-2 and -2/1, get the same equation 10a+4b
Observing the equation, we can have
f(x) are the same.

S(x) has a characteristc, which is
S(x) is a non-increasing fuction in (-1,0) and
S(x) is a non-decreasing fuction in (-infinity,-1),
S(-1) is the maximum, and S(-1)=-1/4 is the solution.