Solving a Quadratic Equation

Hard Algebra Quadratic Equations

Consider the quadratic equation given by:

$$2x^2 - 12x + 18 = 0$$

What are the values of $x$ that satisfy this equation?

Provide the solutions in simplified, fractional form.

$x = 3 + 3\sqrt{2}, \; x = 3 - 3\sqrt{2}$

$x = 6 + 3\sqrt{2}, \; x = 6 - 3\sqrt{2}$

$x = 6, \; x = 3$

$x = 3 + \sqrt{6}, \; x = 3 - \sqrt{6}$

$x = 3 + 3, \; x = 3 - 3$

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