Let's simplify each side of the equation separately:

(5 - x):2 + 3
= (5 - x)/2 + 3
= 5/2 - x/2 + 3
= 2.5 - 0.5x + 3
= 5.5 - 0.5x

(x + 12.2):2
= (x + 12.2)/2
= x/2 + 6.1

Therefore, the equation becomes:

5.5 - 0.5x = x/2 + 6.1

Now let's solve for x:

5.5 - 0.5x = x/2 + 6.1
5.5 - 6.1 = x/2 + 0.5x
-0.6 = 3x/2
-0.6 * 2 = 3x
-1.2 = 3x
-1.2 / 3 = x
x = -0.4

Therefore, the solution to the equation is x = -0.4.