The solutions to 4x^2 + 3 = 3x - 9 can be written in the form x = a \(\pm \)bi, where a and b are real numbers. What is a + b^2? Express your answer as a fraction.

\(\text{straightforward use of the quadratic formula}\\ 4x^2+3=3x-9\\ 4x^2-3x+12=0\\ x = \dfrac{3\pm \sqrt{3^2-4(4)(12)}}{8} = \dfrac 3 8 \pm i \dfrac 1 8 \sqrt{183}\\ a = \dfrac 3 8\\ b= \dfrac{\sqrt{183}}{8}\\ \text{you can calculate }a+b^2\)