I3.4 Let $f\left(\frac{x}{3}\right)=x^{2}+x+1$. If $d$ is the sum of all $x$ for which $f(3 x)=c$, find the value of $d$.
$\begin{aligned} f(x) & =(3 x)^{2}+3 x+1 \\ & =9 x^{2}+3 x+1 \\ f(3 x) & =81 x^{2}+9 x+1 \\ f(3 x) & =21 \\ \Rightarrow & 81 x^{2}+9 x+1=21 \\ \Rightarrow & 81 x^{2}+9 x-20=0 \\ \Rightarrow d & =\text { sum of roots } \\ & =-\frac{9}{81} \\ & =-\frac{1}{9}\end{aligned}$