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(Your computation with) Excel may be not entirely trustworthy... Since you don't tell us what you did "in Excel", we can't help you with this.
BTW, you don't tell us if "the Excel solution" is for $r$ or $\alpha$. But numerically checking this "candidate solution" for either casts a serious doubt on it :
sage: (-300*x^5 + 250*x^4 + 200*x^3 + 150*x^2 + 100*x - 250).subs(x=7.7138).n()
-7.20699223462673e6
sage: (-300*x^5 + 250*x^4 + 200*x^3 + 150*x^2 + 100*x - 250).subs(x=1/7.7138-1).n()
-61.9709622900315
HTH,
