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 = 4√6 ;b = -13 ;c = -2√6

= 4√6.-2√6 = -48

And either of their sum or difference = b

= - 13

Thus the two terms are - 16 and 3

Difference = - 16 + 3 = - 13

Product = - 16.3 = - 48

(On using √6 = √3 √2 and 16 = 4.2.√2 √2 )

⇒ (4√2 x + √3)(√3 x-2√2) = 0

⇒ (4√2 x + √3) = 0 or (√3 x-2√2) = 0

x = (-√3)/(4√2 ) or x = (2√2)/√3

Roots of equation are