Solve the following equations by using formula:

2x² - 7x + 6 = 0

The given equation is 2x² - 7x + 6 = 0.

Comparing it with ax² + bx + c = 0, we get
a = 2 , b = -7 , c = 6

By using formula,

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

we obtain:

$\Rightarrow x = \dfrac{-(-7) ± \sqrt{(-7^2) - 4\times 2 \times 6}}{2 \times 2} \\[1em] \Rightarrow x = \dfrac{7 ± \sqrt{49 - 48}}{4} \\[1em] \Rightarrow x = \dfrac{7 ± \sqrt{1}}{4} \\[1em] \Rightarrow x = \dfrac{7 + 1}{4} \text{ or } \dfrac{7 - 1}{4} \\[1em] \Rightarrow x = \dfrac{8}{4} \text { or } \dfrac{6}{4} \\[1em] x = 2 \text{ or } \dfrac{3}{2}$

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