How do I find x as a function of x?

$$x=462+0.085x$$ $$(1-0.085)x=462$$ $$0.915x=462$$ $$x=\frac{462}{0.915}=\frac{30800}{61}$$

Here you want to solve $$x=462+0.085x$$ There are two equations $y=x$ and $y=462+0.085x$.

Solving for $x=462+0.085x$ is equivalent to determining the solutions for the system $$y=x \text{ (Denoted by Blue Line) }$$

&

$$y=462+0.085x\text{ (Denoted by Red Line) }$$

The point of intersection of those two lines is your solution. Now we proceed to find the solution. $$(1-0.085)x=462$$ $$0.915x=462$$ $$x=\frac{462}{0.915}=\frac{30800}{61}$$