Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = √(3;) b = 11; c = 6√3

= √3.6√3 = 3.6 = 18

(using 3 = √3.√3

And either of their sum or difference = b

= 11

Thus the two terms are 9 and 2

Sum = 9 + 2 = 11

Product = 9.2 = 18

√3 x(x + 3√3) + 2(x + 3√3) = 0

(using 9 = 3.3 = 3√3 √3)

(√3 x + 2)(x + 3√3) = 0

(√3 x + 2)(x + 3√3) = 0

Roots of equation are