The mistake is in the first step. You seem to want to divide through by 7, but you only did it correctly with the x ² term. What you should have after doing this is
7x ² + 9x + 2 = 0
→ x ² + 9/7 x + 2/7 = 0
This step isn't actually necessary to begin with since the starting quadratic is easily factorized:
7x ² + 9x + 2 = (7x + 2) (x + 1) = 0
Then
7x + 2 = 0 or x + 1 = 0
7x = -2 or x = -1
x = -2/7 or x = -1
