Find the point of intersection of the line and surface

I have an odd problem with no solution. I am completely lost on how to solve this.

Problem:

Find the coordinates of the point(s) of intersection of the line

and the surface

Attempt:

(1)

(2)

(3)

Subbing in (1), (2), (3) into the surface i have

Solving i get:

At this point i need to solve for t

It appears to be a quadratic equation.

and

and

Then just plug these t values into the parametric equations to get the points?

Did i do this right?

Re: Find the point of intersection of the line and surface