Final answer:
The quadratic equation 4x^2 - 3x + 3 = 0 has no real-number solutions, because the discriminant is negative. Therefore, none of the options provided are correct solutions.
Step-by-step explanation:
To find the solutions to the given quadratic equation 4x2 - 3x + 3 = 0, we can apply the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a) for any equation of the form ax2 + bx + c = 0. Plugging the values into the formula, where a = 4, b = -3, and c = 3, gives us:
x = (3 ± √((-3)2 - 4(4)(3))) / (2(4))
x = (3 ± √(9 - 48)) / 8
x = (3 ± √(-39)) / 8
Since the discriminant (b2 - 4ac) is negative (-39), this equation has no real-number solutions
Thus, none of the given options A, B, C, D, or E are correct solutions to the equation.