Solve the following equation using quadratic formula:

x² - 10x + 6 = 0

Given,

⇒ x² - 10x + 6 = 0

Comparing equation x² - 10x + 6 = 0 with ax² + bx + c = 0, we get :

a = 1, b = -10 and c = 6.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(-10) \pm \sqrt{(-10)^2 - 4 \times 1 \times (6)}}{2 \times (1)} \\[1em] = \dfrac{10 \pm \sqrt{100 - 24}}{2} \\[1em] = \dfrac{10 \pm \sqrt{76}}{2} \\[1em] = \dfrac{10 \pm \sqrt{19 \times 4}}{2} \\[1em] = \dfrac{10 \pm 2\sqrt{19}}{2} \\[1em] = \dfrac{10 + 2\sqrt{19}}{2} \text{ or } \dfrac{10 - 2\sqrt{19}}{2} \\[1em] = \dfrac{2(5 + \sqrt{19})}{2} \text{ or } \dfrac{2(5 - \sqrt{19})}{2} \\[1em] = 5 + \sqrt{19} \text{ or } 5 - \sqrt{19} \\[1em] = 5 + 4.36 \text{ or } 5 - 4.36 \\[1em] = 9.36 \text{ or } 0.64$

Hence, x = {9.36, 0.64}.