Question

Let $f(x) = \dfrac{2-3x}{5-2x}$. For what value of $a$ is $f(a) = 3$?

Answer 1

I will assume you mean:

f(x) = (2-3x)/(5-2x) and you want to know the value of a so that
f(a) = 36

so (2-3a)/(5-2a) = 36
2 - 3a = 180 - 72a
69a = 178
a = 178/69

check my answer on your calculator by evaluating
f(178/69)

Answer 2

This is a aops problem which is why there are dollar signs (they signify latex)
So dont answer this problem to help a cheater. (reiny was wrong btw because you are solving for a value of a that gives f(a) = 3