Solve for x. I'll do it by completing the square:
2x² = 4x + 9
2x² - 4x = 9
x² - 2x = 9/2
x² - 2x + 1 = 11/2
(x - 1)² = 11/2
x - 1 = ± √(11/2)
x = 1 ± √(11/2)
x = 1 ± √22/2
x = (2 ± √22)/2
Take the solution with the positive square root. Then it follows that a = c = 2 and b = 22. So a + b + c = 26.
