Solve each of the following quadratic equations:

Given: taking LCM

30x^{2} + 30x + 15 = 34x^{2} + 34x cross multiplying

4x^{2} + 4x - 15 = 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 = 4 b = 4 c = - 15

= 4. - 15 = - 60

And either of their sum or difference = b

= 4

Thus the two terms are 10 and - 6

Difference = 10 - 6 = 4

Product = 10. - 6 = - 60

4x^{2} + 4x - 15 = 0

4x^{2} + 10x - 6x - 15 = 0

2x(2x + 5) - 3(2x + 5) = 0

(2x + 5) (2x - 3) = 0

(2x + 5) = 0 or (2x - 3) = 0

Hence the roots of equation are

60