How do you use substitution to make another variable the subject?

Question

I've been trying to solve this question but have no idea how to do it, as we've never covered it before.

"Rewrite the following equation in terms of the new variable"

$$x^2-3x+5=0, y=x-2$$

The goal is to get an equation in the style of $ay^2+by+c=0$

Answer 1

From the second equation we have

$$y=x-2\implies x=y+2$$

and substituting into the first equation gives

$$x^2-3x+5=(y+2)^2-3(y+2)+5=0$$

Can you take it from here?