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√7 ;b = 4 ;c = -√7

= 3√7.-√7 = 3.-7 = -21

(using 7 = √7.√7)

And either of their sum or difference = b

= 4

Thus the two terms are 7 and - 3

Difference = 7 - 3 = 4

Product = 7× - 3 = - 21

( using 7 = √7.√7)

(√7 x-1)(3x + √7) = 0

(√7 x-1) = 0 or (3x + √7) = 0

x = 1/√7 or x = (-7)/√3

Roots of equation are