Solve each of the following quadratic equations:

taking LCM

x + 4 = 2x^{2} + 3x cross multiplying

2x^{2} + 2x - 4 = 0 taking 2 common

x^{2} + x - 2 = 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 = 1 b = 1 c = - 2

= 1. - 2 = - 2

And either of their sum or difference = b

= 1

Thus the two terms are 2 and - 1

Difference = 2 - 1 = 1

Product = 2. - 1 = - 2

x^{2} + x - 2 = 0

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

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

(x + 2) (x - 1) = 0

(x + 2) = 0 or (x - 1) = 0

x = - 2 or x = 1

Hence the roots of equation are - 2 or 1.

53