Solve the following equation using quadratic formula:

2x² - 6x + 3 = 0

Given,

⇒ 2x² - 6x + 3 = 0

Comparing equation 2x² - 6x + 3 = 0 with ax² + bx + c = 0, we get :

a = 2, b = -6 and c = 3.

By formula,

x = $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values we get :

$\Rightarrow x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4 \times 2 \times (3)}}{2 \times (2)} \\[1em] = \dfrac{6 \pm \sqrt{36 - 24}}{4} \\[1em] = \dfrac{6 \pm \sqrt{12}}{4} \\[1em] = \dfrac{6 \pm \sqrt{3 \times 4}}{4} \\[1em] = \dfrac{6 \pm 2\sqrt{3}}{4} \\[1em] = \dfrac{6 + 2\sqrt{3}}{4} \text{ or } \dfrac{6 - 2\sqrt{3}}{4} \\[1em] = \dfrac{2(3 + \sqrt{3})}{4} \text{ or } \dfrac{2(3 - \sqrt{3})}{4} \\[1em] = \dfrac{3 + \sqrt{3}}{2} \text{ or } \dfrac{3 - \sqrt{3}}{2} \\[1em] = \dfrac{3 + 1.73}{2} \text{ or } \dfrac{3 - 1.73}{2} \\[1em] = \dfrac{4.73}{2} \text{ or } \dfrac{1.27}{2} \\[1em] = 2.365 \text{ or } 0.635 \\[1em] \approx 2.37 \text{ or } 0.64$

Hence, x = {2.37, 0.64}.