How to solve this equation- 1/2x-2=1/3(x-2)?

- 1/2x-2=1/3(x-2)

simplify both sides:

-1/2x - 2 = (1/3)x - (1/3)(2)
-1/2x - 2 = (1/3)x - 2/3

group like terms (change the sign when you transpose)

-(1/2)x - (1/3)x = -2/3 + 2

simplify:
[(-3 - 2)/6]x = (-2 + 6)/3
-(5/6)x = 4/3

cross multiply

-5x(3) = (4)(6)
-15x = 24

divide both sides by -15

x = 24/-15

x = -8/5 or -1 3/5

1/(2x - 2) = 1/3(x - 2)
3[2x - 2][1/(2x - 2)] = 3[2x - 2][(x - 2)/3]
3 = [2x - 2][x - 2]
3 = 2x*x - 2*x - 2x*2 + 2*2
2x^2 - 2x - 4x + 4 = 3
2x^2 - 6x + 4 - 3 = 0
2x^2 - 6x + 1 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 2
b = -6
c = 1

x = [6 ±√(36 - 8)]/4
x = [6 ±√28]/4
x = [6 ±5.29]/4 (approx.)

x = [6 + 5.29]/4
x = 11.29/4
x = 2.8225

x = [6 - 5.29]/4
x = 0.71/4
x = 0.1775

∴ x ≈ 0.1775 , 2.8225

Question is unclear.
Could it be :-
(1/2) (x)- 2 = (1/3) (x - 2)
3x - 12 = 2x - 4
x = 8