math problem Lagrange Multiplier Method

With f(x, y, z) = x + 2y + 3z subject to g(x, y, z) = x2 + y2 + z2 - 1:
We set:
Λ(x, y, z) = f(x, y, z) + λg(x, y, z)
= (x + 2y + 3z) + λ(x2 + y2 + z2 - 1)
And the derivatives:
δΛ/δx = 1 + 2λx = 0 → x = -1/2λ
δΛ/δy = 2 + 2λy = 0 → y = -1/λ
δΛ/δz = 3 + 2λz = 0 → z = -3/2λ
δΛ/δλ = x2 + y2 + z2 - 1 = 0
Sub all x, y and z determined into this equation, we have:
x2 + y2 + z2 - 1 = 0
(-1/2λ)2 + (-1/λ)2 + (-3/2λ)2 - 1 = 0
1/(4λ2) + 1/λ2 + 9/(4λ2) = 1
7/(2λ2) = 1
λ2 = 7/2
λ = √(7/2) or -√(7/2)
So the stationary points are;
x = -1/√14, y = -2/√14, z = -3/√14 and
x = 1/√14, y = 2/√14, z = 3/√14