Question

solve for $x$ : $4\sqrt{3} x^2 + 5x - 2\sqrt{3} = 0$

Answer 1

$4\sqrt{3} x^2 + 5x - 2\sqrt{3} = 0 \\ \\ 4 \sqrt{3} {x}^{2} + 8x - 3x - 2 \sqrt{3} = 0 \\ \\ 4x( \sqrt{3} x + 2) - \sqrt{3}( \sqrt{3}x + 2) = 0 \\ \\ ( \sqrt{3} x+ 2)(4x - \sqrt{3}) = 0$

If √3x + 2 = 0

or, √3x = -2

or, x = -2/√3

Either,

4x - √3 = 0

or, 4x = √3

or, x = √3/4

Therefore, the required solutions are

x = -2/√3 , √3/4 .