Given,
⇒ 3 x 2 + 11 x + 6 3 = 0 ⇒ 3 x 2 + 9 x + 2 x + 6 3 = 0 ⇒ 3 x ( x + 3 3 ) + 2 ( x + 3 3 ) = 0 ⇒ ( 3 x + 2 ) ( x + 3 3 ) = 0 ⇒ ( 3 x + 2 ) = 0 or ( x + 3 3 ) = 0 [Using Zero-product rule] ⇒ 3 x = − 2 or x = − 3 3 ⇒ x = − 2 3 or x = − 3 3 . \Rightarrow \sqrt{3}x^2 + 11x + 6\sqrt{3} = 0 \\[1em] \Rightarrow \sqrt{3}x^2 + 9x + 2x + 6\sqrt{3} = 0 \\[1em] \Rightarrow \sqrt{3}x(x + 3\sqrt{3}) + 2(x + 3\sqrt{3}) = 0 \\[1em] \Rightarrow (\sqrt{3}x + 2)(x + 3\sqrt{3}) = 0 \\[1em] \Rightarrow (\sqrt{3}x + 2) = 0 \text{ or } (x + 3\sqrt{3}) = 0 \text{ [Using Zero-product rule] } \\[1em] \Rightarrow \sqrt{3}x = -2 \text{ or } x = -3\sqrt{3} \\[1em] \Rightarrow x = \dfrac{-2}{\sqrt{3}} \text{ or } x = -3\sqrt{3}. ⇒ 3 x 2 + 11 x + 6 3 = 0 ⇒ 3 x 2 + 9 x + 2 x + 6 3 = 0 ⇒ 3 x ( x + 3 3 ) + 2 ( x + 3 3 ) = 0 ⇒ ( 3 x + 2 ) ( x + 3 3 ) = 0 ⇒ ( 3 x + 2 ) = 0 or ( x + 3 3 ) = 0 [Using Zero-product rule] ⇒ 3 x = − 2 or x = − 3 3 ⇒ x = 3 − 2 or x = − 3 3 .
Hence, x = { − 2 3 , − 3 3 } x = \Big{\dfrac{-2}{\sqrt{3}}, -3\sqrt{3}\Big} x = { 3 − 2 , − 3 3 }
