Find
$3 x^{2} - 4 x + 2 = 2 x^{2} - 2 x + 4$

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Solution

$3 x^{2} - 4 x + 2 = 2 x^{2} - 2 x + 4$
$\Rightarrow 3 x^{2} - 2 x^{2} - 4 x + 2 x + 2 - 4 = 0$
$\Rightarrow x^{2} - 2 x - 2 = 0$
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$x = \frac{2 \pm \sqrt{4 - 4 (- 2)}}{2}$
$x = \frac{2 \pm 2 \sqrt{3}}{2}$
$= 1 \pm \sqrt{3}$ .

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