First, simplify the left side of the equation:

(5-10+x-23x-4+39-77+5x):2
=(-77-22x+44):2
=(-22x-33):2
=-11x-16.5

Next, simplify the right side of the equation:

(66-6+3x+2):3
=(60+3x):3
=20+x

Now, set the two simplified expressions equal to each other:

-11x-16.5 = 20+x

Combine like terms:

-12x - 16.5 = 20

Add 16.5 to both sides:

-12x = 36.5

Divide by -12:

x = -3.04166666667

Therefore, the solution to the equation is x = -3.04166666667.