Step 1 :Let's denote the total amount Brian has invested as x. Then, half of his investments would be 0.5x. The total annual interest from the 10% dividend stock would be 0.10 * 0.5x and from the 14% interest stock would be 0.14 * 0.5x. The sum of these two amounts is equal to $780.
Step 2 :So, we have the equation: 0.10 * 0.5x + 0.14 * 0.5x = 780.
Step 3 :We can solve this equation to find the value of x, which is the total amount Brian has invested.
Step 4 :The solution to the equation is 6500. This means that Brian has $6500 invested in total.
Step 5 :Final Answer: The total amount Brian has invested is \(\boxed{6500}\).