Question

Solve for $x$:

$3-3\sqrt{3}+4\sqrt{3}x\left(\frac{3\sqrt{5}}{34\sqrt{3}}\right)=0$

Answer 1

Consider the given equation,

$3-\sqrt{3}.3+4\sqrt{3}x\frac{3\sqrt{5}}{34\sqrt{3}}=0$

$3-\sqrt{3}.3=-4\sqrt{3}x\frac{3\sqrt{5}}{34\sqrt{3}}$

$3-\sqrt{3}.3=-2x\frac{3\sqrt{5}}{17}$

$x=\frac{-17(3-\sqrt{3}.3)}{2\times 3\sqrt{5}}=\frac{17\times 3(\sqrt{3}-1)}{6\sqrt{5}}$

$x=\frac{17(\sqrt{3}-1)}{2\sqrt{5}}$

Hence, this is the answer.