I assume the _ characters are supposed to be minus signs, as in
3x ² + 3y ² - 7x - 6y - 3 = 0
Move the 3 to the right sides, and complete the square in x and y :
(3x ² - 7x) + (3y ² - 6y ) = 3
3 (x ² - 7/3 x) + 3 (y ² - 2y ) = 3
x ² - 7/3 x + y ² - 2y = 1
(x ² - 7/3 x + 49/36) + (y ² - 2y + 1) = 1 + 49/36 + 1
(x - 7/6)² + (y - 1)² = 121/36
(x - 7/6)² + (y - 1)² = (11/6)²
The circle thus has radius 11/6, so its diameter is 2 • 11/6 = 11/3.