Solve the following equation using quadratic formula:

x² - 4x + 1 = 0

Comparing equation x² - 4x + 1 = 0 with ax² + bx + c = 0, we get :

a = 1, b = -4 and c = 1.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times 1}}{2 \times 1} \\[1em] = \dfrac{4 \pm \sqrt{16 - 4}}{2} \\[1em] = \dfrac{4 \pm \sqrt{12}}{2} \\[1em] = \dfrac{4 \pm \sqrt{4 \times 3}}{2} \\[1em] = \dfrac{4 \pm 2\sqrt{3}}{2} \\[1em] = \dfrac{2(2 \pm \sqrt{3})}{2} \\[1em] = 2 \pm \sqrt{3} \\[1em] = 2 + \sqrt{3} \text{ or } 2 - \sqrt{3}.$

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