Let's first simplify the equation:

9.8(4.7-x) + 1.2(5+x) = 13

43.16 - 9.8x + 6 + 1.2x = 13

49.16 - 8.6x = 13

Next, move all constants to one side of the equation and all variables to the other side:

49.16 - 13 = 8.6x

36.16 = 8.6x

Now, divide by 8.6 to solve for x:

x = 36.16 / 8.6

x = 4.21

Therefore, the value of x that satisfies the equation is x = 4.21.