Solve the following equation using quadratic formula:

4x² - 7x + 2 = 0

Given,

⇒ 4x² - 7x + 2 = 0

Comparing equation 4x² - 7x + 2 = 0 with ax² + bx + c = 0, we get :

a = 4, b = -7 and c = 2.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(-7) \pm \sqrt{(-7)^2 - 4 \times (4) \times (2)}}{2 \times (4)} \\[1em] = \dfrac{7 \pm \sqrt{49 - 32}}{8} \\[1em] = \dfrac{7 \pm \sqrt{17}}{8} \\[1em] = \dfrac{7 + \sqrt{17}}{8} \text{ or } \dfrac{7 - \sqrt{17}}{8} \\[1em] = \dfrac{7 + 4.12}{8} \text{ or } \dfrac{7 - 4.12}{8} \\[1em] = \dfrac{11.12}{8} \text{ or } \dfrac{2.88}{8} \\[1em] = 1.39 \text{ or } 0.36$

Hence, x = {1.39, 0.36}.