No problem to plot it. Note that I moved the -1 on the right hand side to the left of the equality so that ezplot can handle it.
HOWEVER... IF you want to solve for values of x such that this curve crosses the y axis, Note that the plot never seems to cross the y axis. There are no values of x such that y is zero.
If you want to solve for pairs of points (x,y) that solve the nonlinear equation, there are infinitely many such solutions. In fact, for any value of x, there are at least two such solutions, and I see 4 solutions (for x near zero.)
Similarly, if you choose to fix ANY value of y, there will be zero or two real solutions, since what remains will be a quadratic polynomial in x.
Note that solve itself must fail to produce all those solutions. In fact, the solution that luc proposes indeed does fail to produce the full set. So beware, as solve does NOT always produce all valid solutions for something like this.