Answer:
n = 2 or n = -3/2
Step-by-step explanation by completing the square:
Solve for n:
2 n^2 - n - 6 = 0
Divide both sides by 2:
n^2 - n/2 - 3 = 0
Add 3 to both sides:
n^2 - n/2 = 3
Add 1/16 to both sides:
n^2 - n/2 + 1/16 = 49/16
Write the left hand side as a square:
(n - 1/4)^2 = 49/16
Take the square root of both sides:
n - 1/4 = 7/4 or n - 1/4 = -7/4
Add 1/4 to both sides:
n = 2 or n - 1/4 = -7/4
Add 1/4 to both sides:
Answer: n = 2 or n = -3/2