Solve each of the following quadratic equations:

√7x^{2} – 6x – 13√7 = 0

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

= √7.-13√7 = -13.7 = -91

And either of their sum or difference = b

= - 6

Thus the two terms are 7 and - 13

Difference = - 13 + 7 = - 6

Product = 7. - 13 = - 91

x(√7 x-13) + √7 (√7 x-13) = 0

(x + √7)(√7 x-13) = 0

(x + √7) = 0 or (√7 x-13) = 0

x = -√7 or x = 13/√7

Roots of equation are

24