Given:

taking LCM

using (a - b)² = a² + b² - 2ab

8x² - 8x + 4 = 17x² - 17x cross multiplying

9x² - 9x - 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 = 9 b = - 9 c = - 4

= 9. - 4 = - 36

And either of their sum or difference = b

= - 9

Thus the two terms are - 12 and 3

Sum = - 12 + 3 = - 9

Product = - 12.3 = - 36

9x² - 9x - 4 = 0

9x² - 12x + 3x - 4 = 0

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

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

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

Hence the roots of equation are