Find Solution to x^2 + x - 2=0

Using the factorisation method.

the factorised solution will look like (x+a)(x+b) = 0

by multiplying these two brackets we get the equation:

x^2 + a.x+b.x + a.b = 0

so vomparing this to the equation in the question we see

a.b = -2        and       a+b = 1    and   a = -2/b

using substitution:

b^2 - 2 = b

b(b-1) = 2      so     b=2   (try substituting this in)

if b = 2 then a = -1

so the solution is 

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