Not sure if the way I proved something is correct.

[final pawn]

Im trying to solve this exercise where it says:
prove that if x,y are real numbers ∀x∃y(2y=x2+x)
i solved it like:
y = (x^2 + x)/2
so 2(x^2 + x) / 2 = x^2 + x
meaning that :
x^2 + x = x^2 + x
and that is true because
x^2 + x - x^2 + x = 0 .
so there will always exist at least one y for all x that satisfies the equation...
Is this proof enough? or am i missing anything? I dont even know what method that is.. it just seems logical ...

[final pawn]

I still need a bit of reassurance lmao

[dull jacinth]

I think that that's enough but you made a small error in your last equation

[acoustic shuttle]

.solved