To solve this equation, we first need to simplify the left side of the equation:

5x^2 - 3(x^2 + 2x) + 3x + 9 = 14

Distribute the -3 on the terms inside the parentheses:

5x^2 - 3x^2 - 6x + 3x + 9 = 14

Combine like terms:

2x^2 - 3x + 9 = 14

Now, subtract 14 from both sides:

2x^2 - 3x - 5 = 0

This equation cannot be solved by simple factoring, so we can use the quadratic formula to find the values of x:

x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2))
x = (3 ± √(9 + 40)) / 4
x = (3 ± √49) / 4
x = (3 ± 7) / 4

Therefore, the two solutions are:

x = (3 + 7) / 4 = 10 / 4 = 2.5
x = (3 - 7) / 4 = -4 / 4 = -1

So, the solutions to the equation are x = 2.5 and x = -1.