Find an equation of the plane that passes through the points $(1, 2, 5), (5, 4, 8) \textrm{ and } (2, 4, 8)$ Find an equation of the plane that passes through the points $(1, 2, 5), (5, 4, 8) $, and $(2, 4, 8)$.
$v_1 = [1,2,5] - [5,4, 8] = [-4, -2, -3]$
$v_2 = [2,4,8] - [5,4,8] = [-3,0,0]$
$v_1 \times v_2 = [0,9,-6]$
thus,
$ax + by + cz = d, a = 0, b = 9, c = -6$
to get d we plug $0(5) + 9(4) - 6(8) = -12$
Therefore the equation is $9y - 6z = -12$ 
Right?

Yes, your answer is correct. 
Note that if $P(x,y,z)$ is on the plane passing through your given points then then the volume generated by vectors $$  (x-1,y- 2,z- 5), (x-5,y- 4,z- 8),  (x-2,y- 4,z- 8)$$ is zero.
Thus the equation of the plain is:
$$ \det \begin{bmatrix} x-1&y-2 &z-5\\x-5&y-4&z-8\\x-2&y-4&z-8\end{bmatrix} =0$$ 
