You have defined positive direction as moving to the left. That's OK, but placing a plus sign in front of the value for tension in the rope means that you think is pushing to the left. But it can't - it's a rope! It must be in tension, trying to pull the block to the right - so the sign of the 784N force, due to tension in the rope, should negative.
I strongly suggest that for this problem, and the others you have posted recently, you should ALWAYS draw a free-body diagram of forces acting on the body of interest. This will help you see which way forces are acting on the body, and will allow you to determine the correct sign to use for each force.
Total force acting down the slope ignoring friction for the moment is
150 + 100*9.81*sin 20 - 784 = -299.3
The negative sign says that the sum of these forces is actually pulling to the right. Meaning the block will try to slide uphill, IF it can overcome static friction.
Next: is this force enough to overcome static friction?
F_s = 0.2 *100 * 9.81 *cos(20) = 276.6N. Since the upward force is greater than this, the block is moving. Now we can use sliding friction in the sum of forces:
Total F = -299.3 + 0.2 x 100 x 9.81 x cos(20) = -299.3 + 184.4 = -114.9N. Again, the minus sign says the sum of forces is upward, and the block slides up the ramp.