solving x in a polynomial function

help.search("polynomial")
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Sent from my phone. Please excuse my brevity.

Hi there,

Does anyone know how I solve for x from a given y in a polynomial
function? Here's some example code:

##example file

a<-1:10

b<-c(1,2,2.5,3,3.5,4,6,7,7.5,8)

po.lm<-lm(a~b+I(b^2)+I(b^3)+I(b^4)); summary(po.lm)

(please ignore that the model is severely overfit- that's not the
point).

Let's say I want to solve for the value b where a = 5.5.

Any thoughts? I did come across the polynom package, but I don't think
that does it- I suspect the answer is simpler than I am making it out
to be. Any help would be welcome.