Solve the following equations by using formula:

2x² - 6x + 3 = 0

The given equation is 2x² - 6x + 3 = 0.

Comparing it with ax² + bx + c = 0, we get
a = 2 , b = -6 , c = 3

By using formula,

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

we obtain:

$\Rightarrow x = \dfrac{-(-6) ± \sqrt{(-6^2) - 4\times 2 \times 3}}{2 \times 2} \\[1em] \Rightarrow x = \dfrac{6 ± \sqrt{36 - 24}}{4} \\[1em] \Rightarrow x = \dfrac{6 ± \sqrt{12}}{4} \\[1em] \Rightarrow x = \dfrac{6 + \sqrt{12}}{4} \text{ or } \dfrac{6 - \sqrt{12}}{4} \\[1em] \Rightarrow x = \dfrac{6 + 2\sqrt{3}}{4} \text { or } \dfrac{6 - 2\sqrt{3}}{4} \\[1em] x = \dfrac{3 + \sqrt{3}}{2} \text{ or } \dfrac{3 - \sqrt{3}}{2}$

Hence roots of the given equation are $\dfrac{3 + \sqrt{3}}{2} , \dfrac{3 - \sqrt{3}}{2}$.