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f(x)=x^4+ax^3+bx^2+cx+d. If alpha < beta...

`f(x)=x^4+ax^3+bx^2+cx+d.` If `alpha < beta < gamma < delta` are distinct positive integers greater than 3 such that `f(alpha)=fbeta)=f(gamma)=f(delta)=0 and 8a+4b|b+2c+d=1139,` then find sum `(alpha+beta+gamma+delta)``

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