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

5x^2 - 3(x^2 + 2x) + 3x + 9
5x^2 - 3x^2 - 6x + 3x + 9
2x^2 - 6x + 9

Now we substitute this simplified expression back into the original equation:

2x^2 - 6x + 9 = 14

Next, we move the constant term to the other side of the equation:

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

Now we set the equation equal to zero by subtracting 5 from both sides:

2x^2 - 6x - 5 = 0

This quadratic equation can be solved using the quadratic formula:

x = (-(-6) ± √((-6)^2 - 4(2)(-5))) / (2(2))
x = (6 ± √(36 + 40)) / 4
x = (6 ± √76) / 4
x = (6 ± 2√19) / 4
x = (3 ± √19) / 2

Therefore, the solutions to the equation are x = (3 + √19) / 2 and x = (3 - √19) / 2.