Final answer:
The quadratic equation 3x^2 - 8x + 4 = 0 is solved using the quadratic formula, resulting in two solutions for x, which are 2 and 2/3.
Step-by-step explanation:
The student's question involves determining which values of x satisfy a given quadratic equation. The equation provided seems to have a typographical error, but it resembles the form 3x^2 - 8x + 4 = 0. To solve this quadratic equation, we can apply the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax^2 + bx + c = 0.
In our case, a = 3, b = -8, and c = 4. Plugging these values into the quadratic formula gives us:
x = (-(-8) ± √((-8)^2 - 4(3)(4))) / (2(3))
x = (8 ± √(64 - 48)) / 6
x = (8 ± √16) / 6
x = (8 ± 4) / 6
So, the two possible solutions for x are:
x = (8 + 4) / 6 = 12/6 = 2
x = (8 - 4) / 6 = 4/6 = 2/3
Therefore, the values of x that satisfy the equation are 2 and 2/3.