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 = 1; b = 2√2; c = -6

= 1. - 6 = - 6

And either of their sum or difference = b

= 2√2

Thus the two terms are 3√2 and -√2

Difference = 3√2-√2 = 2√2

Product = 3√2.-√2 = 3.-2 = -6

using

x(x + 3√2)-√2(x + 3√2) = 0

(x-√2)(x + 3√2) = 0

(x-√2) = 0 or (x + 3√2) = 0

x = √2 or x = -3√2

Roots of equation are √2 or -3√2