Solve my shit

So I'm taking a course on Precalc, and learning how to invert functions. Then I come across this gem of a problem:
f(x) = x((x+2)/5)
After substitution I get
f^-1(x) = 5(x/(f^-1(x)))-2
wat.
Of course my tiny brain possesses a very minimal understanding of what I've just done. I asked one kid in my class who told me that the original function is actually f(x) = (x²+2x)/5, and then another kid who told me to go fuck myself as this is a non-invertible function.
Halp

y = x((x+2)/5)
y = x^2/5 + 2x/5
5y = x^2 + 2x
5y = (x + 1)^2 - 1
5y + 1 = (x + 1)^2
x + 1 = ±sqrt(5y + 1)
x = -1 ±sqrt(5y + 1)

It's the closest you can get to a function. It's still not a function, since you don't have any x value for y < -1/5 and you have two x values for every y strictly larger than that.

HTH