Solve the following equations by using formula:

2x² - 3x - 1 = 0

The given equation is 2x² - 3x - 1 = 0

Comparing it with ax² + bx + c = 0
a = 2, b = -3, c = -1

By using the formula , x = $\dfrac{-b ± \sqrt{b^2 - 4ac}}{2a}$ , we obtain

$\Rightarrow \dfrac{-(-3) ± \sqrt{(-3)^2 - 4 \times 2 \times -1 }}{2 \times 2} \\[1em] \Rightarrow \dfrac{3 ± \sqrt{9 + 8}}{4} \\[1em] \Rightarrow \dfrac{3 + \sqrt{17}}{4} \text{ or } \dfrac{3 - \sqrt{17}}{4} \\[1em]$

Hence, roots of the equation are $\dfrac{3 + \sqrt{17}}{4} , \dfrac{3 - \sqrt{17}}{4}$.