Solve each of the following quadratic equations:

Given:

taking LCM

using (a - b)^{2} = a^{2} + b^{2} - 2ab

cross multiplying

18x^{2} - 48x + 130 = 105x - 140

18x^{2} - 153x + 270 = 0 taking 9 common

2x^{2} - 17x + 30 = 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 = 2 b = - 17 c = 30

= 2.30 = 60

And either of their sum or difference = b

= - 17

Thus the two terms are - 12 and - 5

Sum = - 12 - 5 = - 17

Product = - 12. - 5 = 60

2x^{2} - 17x + 30 = 0

2x^{2} - 12x - 5x + 30 = 0

2x(x - 6) - 5(x - 6) = 0

(x - 6) (2x - 5) = 0

(x - 6) = 0 or (2x - 5) = 0

Hence the roots of equation are

58