We can use quadratic formula to determine the roots of the given quadratic equation.
The quadratic formula is:
[tex]x= \frac{-b+- \sqrt{ b^{2} -4ac} }{2a} [/tex]
b = coefficient of x term = 12
a = coefficient of squared term = 4
c = constant term = 9
Using the values, we get:
[tex]x= \frac{-12+- \sqrt{144-4(4)(9)} }{2(4)} \\ \\
x= \frac{-12+-0}{8} \\ \\
x= \frac{-3}{2} [/tex]
So, the correct answer to this question is option B
