To solve this equation, we need to follow the order of operations (PEMDAS).

First, let's simplify the left side of the equation:

83 x 56 - 780 ÷ 13 - 4588
= 4648 - 60 - 4588
= 88

Now, let's simplify the right side of the equation:

1256 x 4 + 23 x 78
= 5024 + 1794
= 6818

Now we have:

88x = 6818

To find the value of x, we need to divide both sides by 88:

x = 6818 / 88
x = 77.75

Therefore, the solution to the equation is x = 77.75.