  We consider the problem of efficiently solving a system of $n$ non-linear
equations in ${\mathbb R}^d$. Addressing Smale's 17th problem stated in 1998,
we consider a setting whereby the $n$ equations are random homogeneous
polynomials of arbitrary degrees. In the complex case and for $n= d-1$,
Beltr\'{a}n and Pardo proved the existence of an efficient randomized algorithm
and Lairez recently showed it can be de-randomized to produce a deterministic
efficient algorithm. Here we consider the real setting, to which previously
developed methods do not apply. We describe an algorithm that efficiently finds
solutions (with high probability) for $n= d -O(\sqrt{d\log d})$. If the maximal
degree is very large, we also give an algorithm that works up to $n=d-1$.
