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Question:

Solve for x: 3x² - √6x + 2 = 0

Solution:

The given quadratic equation is 3x² - √6x + 2 = 0
Comparing with the quadratic equation ax² + bx + c = 0, we have
a = 3, b = -√6, c = 2
Discriminant of the given quadratic equation, D = b² - 4ac ⇒ (-√6)² - 4(3)(2) = 6 - 24 = -18
Therefore, x = -b ± √D / 2a
x = -(-√6) ± √-18 / 2(3)
x = √6 ± 3√2i / 6
x = (√6 ± 3√2i) / 6