Let's solve this equation step by step.
First, distribute the 800 to the terms inside the parentheses:
800 - 480X(1 - X) = 80
Next, distribute the 480X to the terms inside the parentheses:
800 - 480X + 480X^2 = 80
Combine like terms:
480X^2 - 480X + 720 = 0
Now, let's solve this quadratic equation. We can factor out a common factor of 240:
240(2X^2 - 2X + 3) = 0
The equation is equal to zero if either 240 or (2X^2 - 2X + 3) is equal to zero.
Setting 240 equal to zero gives no solutions.
Setting (2X^2 - 2X + 3) equal to zero:
2X^2 - 2X + 3 = 0
Using the quadratic formula, X = (-b +/- sqrt(b^2 - 4ac))/(2a), where a = 2, b = -2, and c = 3:
X = (-(-2) +/- sqrt((-2)^2 - 4(2)(3)))/(2(2))
X = (2 +/- sqrt(4 - 24))/4
X = (2 +/- sqrt(-20))/4
Since sqrt(-20) is imaginary and the equation only asks for real solutions, there are no real solutions for this equation.
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