The equation of a circle is 3x^2+3y^2_7x_6y_3=0.Find the length of its diameter.​

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.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11