To solve the inequality -4x² + 12x - 11 > 0, we can use the quadratic formula or factor the quadratic expression.

Using the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / (2a)

For the quadratic expression -4x² + 12x - 11, a = -4, b = 12, and c = -11.

x = (-12 ± √(12² - 4(-4)(-11))) / (2(-4))
x = (-12 ± √(144 - 176)) / (-8)
x = (-12 ± √(-32)) / (-8)

Since the discriminant is negative, there are no real solutions. Therefore, there are no x-values that satisfy the inequality -4x² + 12x - 11 > 0.