Solve each of the following quadratic equations:

Given:

taking LCM

3x^{2} - 33x + 87 = 5x^{2} - 60x + 175 cross multiplying

2x^{2} - 27x + 88 = 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 = - 27 c = 88

= 2.88 = 176

And either of their sum or difference = b

= - 27

Thus the two terms are - 16 and - 11

Sum = - 16 - 11 = - 27

Product = - 16. - 11 = 176

2x^{2} - 27x + 88 = 0

2x^{2} - 16x - 11x + 88 = 0

2x(x - 8) - 11(x - 8) = 0

(x - 8) (2x - 11) = 0

(x - 8) = 0 or (2x - 11) = 0

Hence the roots of equation are

61