Let's solve this equation step by step:

Distribute the terms on the right side:
3.5 - 2x + 7.5x = 6x - (30 - 12x - 5x + 14x^2)

Simplify the right side:
3.5 + 5.5x = 6x - (30 - 12x - 5x + 14x^2)
8.5x + 3.5 = 6x - 30 + 12x + 5x - 14x^2

Combine like terms:
8.5x + 3.5 = 23x - 30 - 14x^2

Move all terms to one side of the equation:
14x^2 + 8.5x - 23x + 3.5 + 30 = 0
14x^2 - 14.5x + 33.5 = 0

Solve the quadratic equation using the quadratic formula:
x = (-(-14.5) ± √((-14.5)^2 - 41433.5))/(2*14)
x = (14.5 ± √(210.25 - 1876))/28
x = (14.5 ± √(-1665.75))/28
Since the discriminant is negative, there are no real solutions to this equation.

Therefore, the original equation has no real solutions.