First, let's simplify both sides of the equation:

2x² - 3x + 104 = -3x² - 48 + 4
2x² - 3x + 104 = -3x² - 44

Now, let's move all the terms to one side of the equation to set it equal to zero:

2x² - 3x + 104 + 3x² + 44 = 0
5x² - 3x + 148 = 0

Now that we have a quadratic equation, we can solve for x. We can either factor the equation or use the quadratic formula:

x = [3 ± √(3² - 4(5)(148))] / (2(5))
x = [3 ± √(9 - 2960)] / 10
x = [3 ± √(-2951)] / 10

Since the discriminant is negative, there are no real roots for this equation.