Given:

taking LCM; using (a + b)² = a² + b² + 2ab

- 24x² - 64x - 1 = 3(8x² - 2x - 3) cross multiplying

- 24x² - 64x - 1 = 24x² - 6x - 9

48 x² + 58x - 8 = 0 taking 2 common

24 x² + 29x - 4 = 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 a = 24 b = 29 c = - 4

= 24. - 4 = - 96

And either of their sum or difference = b

= 29

Thus the two terms are 32 and - 3

Difference = 32 - 3 = 29

Product = 32. - 3 = - 96

24 x² + 29x - 4 = 0

24 x² + 32x - 3x - 4 = 0

8x(3x + 4) - 1(3x + 4) = 0

(3x + 4)(8x - 1) = 0

(3x + 4) = 0 or (8x - 1) = 0

Hence the roots of equation are