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The equation 0 = 3x^2 - 5x - 5 can be rewritten in the standard quadratic form as 3x^2 - 5x - 5 = 0.
To find the number of real-number solutions, we can use the discriminant formula:
Discriminant = b^2 - 4ac
where a = 3, b = -5, and c = -5.
Plugging in the values, we get Discriminant = (-5)^2 - 4*3*(-5) = 25 + 60 = 85
Since the discriminant is a positive number (85), the equation has two distinct real number solutions.