In this talk i will report two results on searching for polynomial patterns within subsets of the reals. Let P(t) be a polynomial. i will talk about how to find patterns of the form (x, t+t, x+P(t)) in positive density subsets of the reals. Moreover, I will also talk about searching for patterns of the same form within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint works with Polona Durcik and Joris Roos, and with Rob Fraser and Malabika Pramanik.