Parametric equations, eliminating the parameter $x = t^2 + t$ $y= 2t-1$

Parametric equations, eliminating the parameter $x = t^2 + t$ $y= 2t-1$

$$x = t^2 + t$$ $$y= 2t-1$$
So I solve y for t
$$t = \frac{1}{2}(y+1)$$
Then I am suppose to plug it into the equation for x which is where I lose
track of the logic.
$$x = ( \frac{1}{2}(y+1))^2 + \frac{1}{2}(y+1) = \frac{1}{4}y^2 +
y+\frac{3}{4}$$
That is now my answer? I am lost. This is x(y)? How is this valid? I don't
understand.