Solve the equation 9x² + $\dfrac{3x}{4} + 2$ = 0, if possible, for real values of x.

Given,

9x² + $\dfrac{3x}{4} + 2$ = 0

$\Rightarrow \dfrac{36x^2 + 3x + 8}{4} = 0$

⇒ 36x² + 3x + 8 = 0

Comparing 36x² + 3x + 8 = 0 with ax² + bx + c = 0 we get,

a = 36, b = 3 and c = 8

D = b² - 4ac = (3)² - 4(36)(8) = 9 - 1152 = -1143.

Since, D < 0 hence, roots are imaginary.

There is no possibility of real roots.