How do I solve this (re-written, rational equations using quadratic formula)?

Question

2x - 1 / 5 - 2 / x = x / 2

I wrote it wrong the first time, this is the re-post.

Answer 1

2x -1/5 -2/x = x/2
multiply both sides by x
2x^2-x/5-2=x^/2
subtract x^2/2 from both sides
1.5x^2-x/5-2=0
which is in the form
ax^2+bx+c=0
use quadratic formula to solve for x

Answer 2

Reading this as:-
(2x - 1) / 5 - 2 / x = x / 2
2x.(2x - 1) - 20 = 5x²
4x² - 2x - 20 = 5x²
x² + 2x + 20 = 0
x = [- 2 ± √ (-76) ] / 2
x = [- 2 ± √(76 i²)] / 2
x = [- 2 ± 2√19 i ] / 2
x = - 1 ± √19 i