Algebra Level 3

Consider the quadratic polynomial $$f(x)=a{ x }^{ 2 }+bx+c$$ ($$a\neq 0$$).

It's given that $$a\lt b$$ and for every real $$x$$, we have $$f(x)\geq 0$$.

Find the minimum possible value of $$\dfrac{ a+b+c }{ b-a }$$ .

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