To solve the equation, we first need to simplify it by combining like terms on both sides:

5x^2 - 9x + 14 = 3x^2 + 2x - 1

Subtract 3x^2 from both sides:

5x^2 - 9x + 14 - 3x^2 = 2x - 1

2x^2 - 9x + 14 = 2x - 1

Now, subtract 2x from both sides:

2x^2 - 9x + 14 - 2x = -1

2x^2 - 11x + 14 = -1

Next, add 1 to both sides:

2x^2 - 11x + 14 + 1 = 0

2x^2 - 11x + 15 = 0

Now, the equation is in standard form (ax^2 + bx + c = 0) and we can solve for x using the quadratic formula:

x = (-(-11) ± √((-11)^2 - 4(2)(15)))/(2(2))

x = (11 ± √(121 - 120))/4

x = (11 ± √1)/4

x = (11 ± 1)/4

x = (11 + 1)/4 or x = (11 - 1)/4

x = 12/4 or x = 10/4

x = 3 or x = 2.5

Therefore, the solutions to the equation are x = 3 and x = 2.5.