Final answer:
The solutions for the equation -2x^2 + 3x - 9 = 0 are complex numbers.
Step-by-step explanation:
The equation is: -2x^2 + 3x - 9 = 0
To solve this quadratic equation, we can use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -2, b = 3, and c = -9. Substituting these values into the quadratic formula, we have:
x = (-3 ± √((3)^2 - 4(-2)(-9))) / (2(-2))
x = (-3 ± √(9 - 72)) / (-4)
x = (-3 ± √(-63)) / (-4)
The discriminant (b^2 - 4ac) is negative, which means there are no real solutions. The solutions are complex.
Therefore, the solutions for this equation are: x = (3 ± √(63)i) / -4