how to convert explicit function to implicit?

Hi, I have an equation and I want y be as a fuction, in fact, I 'd like a function in which x is independent variable and y is dependent to x,could you please help me how to do it?

A is a complicated equation but doesn't have "y" in it so it is not important what it is, a and b also have values.

[Rik]

This seems doable with fairly basic algebra. What have you tried so far?

[M]

it seems simple but when I tried to solve by hand, it becomes complicated...

Answer 1

[Wan Ji]

If you feel bored solving it by hand, just use matlab!

syms a y x b A
eq = a*y - x*(a+1) - A*(x^2-b*a^2*(y-x)^2);
y = solve(eq, y)

the answer is

y =
 
 -((4*b*A^2*x^2 + 4*b*A*x + 1)^(1/2) - 2*A*a*b*x + 1)/(2*A*a*b)
  ((4*b*A^2*x^2 + 4*b*A*x + 1)^(1/2) + 2*A*a*b*x - 1)/(2*A*a*b)

[M]

Many thanks, yeah, it is complicated by hand