Calculus 3 question: finding equation of tangent plane?

Question

Find the equation of the tangent plane to x^2+y^2+z^2 = 7z at the point (3,-1,2)

*The answer is 6x-2y-3z=10, but I don't know how to do this problem. Please show me the steps.
Thanks.

Answer 1

Take the derivative of that thing with respect to x...

2x (and plug 3 in it) = 6

...with respect to y...

2y (and plug -1 in it) = -2

...with respect to z...

2z - 7 (and plug 2 in it) = -3

You have your coefficients to x,y,z: (6,-2,-3)

Answer 2

The coefficients are calculated as given in the former answer but the equation is
6(x-3)-2(y+1)-3(z-2)=0 so 6x-2y-3z=18-2-6=10