Find the equation of the plane tangent to the graph of the function

z(x,y) = 7(x^2) − 6(y^2) − 7x + 4y + 7 at the point (x,y)=(9,9)

the z(x,y) is throwing me off since it isnt f(x,y). Is there any difference?

I've done this problem about a million time, and am still not getting the right answer.

my solution:

there is no value for z though which confuses me.

I know that an equation of the tangent plane to the surface z = f(x,y) at the point

is

but when I plug in everything into this equation I get

which is wrong. Any help would be appreciated.