How do i find all real solutions

How do i find all real solutions?

1 / x-1 + 1/ x+2 = 5/4

Next time, use properly parentheses!

1/(x - 1) + 1/(x + 2) = 5/4

lcd = 4*(x - 1)*(x + 2)

4*(x + 2) + 4*(x - 1) = 5*(x - 1)*(x + 2)

4*x + 8 + 4*x - 4 = 5*(x^2 + x - 2)

8*x + 4 - 5*x^2 - 5*x + 10 = 0

- 5*x^2 + 3*x + 14 = 0

(5*x + 7)*(x - 2) = 0

5*x + 7 = 0, x1 = - 7/5

x - 2 = 0, x2 = 2