The teacher will be very surprised to see your correct solution 😉
2 2 2 8*y + 9*x + 50*z - 30*x*z - 12*x*y + 8*y*z = 0
9*x^2 - 12*x*y - 30*x*z + 8*y^2 + 8*y*z + 50*z^2 = 0