Note that $$x+2x^2 + 3x^3 + \cdots = (x+x^2+x^3+\cdots)(1+x+x^2+\cdots)=\Big(\frac{1}{1-x} -1\Big)\Big(\frac{1}{1-x}\Big)=20$$ Let $y=\frac{1}{1-x}$, then $$ (y-1)(y)=20\implies y=5,4\implies x=\frac{4}{5}, \frac{5}{4}$$ However $x=\frac{5}{4}$ will diverge. Therefore the answer is $\boxed{\frac{4}{5}}$.