To solve the equation 2a\(^2\) - 3a - 27 = 0, we can use the quadratic formula which is:
a = (-b ± sqrt(b\(^2\) - 4ac)) / 2a
In this case, we have a = 2, b = -3, and c = -27. Substituting these values into the formula, we get:
a = (-(-3) ± sqrt((-3)\(^2\) - 4(2)(-27))) / 2(2)
Simplifying the expression under the square root, we get:
a = (-(-3) ± sqrt(225)) / 4
which gives us:
a = (3 ± 15) / 4
Therefore, we have two solutions:
a = 3 and a = -6/2 = -3/2
Hence, the correct option is -3, 9/2.