Solve each of the following quadratic equations:

Given:

taking LCM

cross multiplying

3x^{2} - 5x = 6x^{2} - 18x + 12

3x^{2} - 13x + 12 = 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 = 3 b = - 13 c = 12

= 3.12 = 36

And either of their sum or difference = b

= - 13

Thus the two terms are - 9 and - 4

Sum = - 9 - 4 = - 13

Product = - 9. - 4 = 36

3x^{2} - 13x + 12 = 0

3 x^{2} - 9x - 4x + 12 = 0

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

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

Hence the roots of equation are

63