Fibonacci's proof that $x^3+2x^2+10x=20$ has no solution in radicals? I read on a poster today that Fibonacci showed that $x^3+2x^2+10x=20$ has no solution expressible in radicals, way back when.
I couldn't find the proof anywhere. Does anyone know where I can find it? 

He proved that the solution cannot be one of Euclid's irrationals. All Euclid's irrationals are strictly contained in the set of numbers of the form
$$
\sqrt[4]{p}\pm\sqrt[4]{q},
\qquad p,q\in\mathbb{Q}.
$$
The proof would be similar to (but of course more complicated than) how you prove $\sqrt2$ is not rational.
