Question

Solve for $x$:
$\sqrt{3}{x}^2-2\sqrt{2}x-2\sqrt{3}=0$

Answer 1

We know that $a{x}^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\sqrt{3}{x}^2-2\sqrt{2}x-2\sqrt{3}=0$

$x=\frac{-(-2\sqrt{2})\pm \sqrt{(-2{\sqrt{2}}^2-4\times \sqrt{3}\times (-2\sqrt{3}\left)\right)}}{2\sqrt{3}}$

$=\frac{2\sqrt{2}\pm \sqrt{8+24}}{2\sqrt{3}}$

$=\frac{2\sqrt{2}\pm \sqrt{32}}{2\sqrt{3}}$

$=\frac{2\sqrt{2}\pm 4\sqrt{2}}{2\sqrt{3}}$

$=\frac{\sqrt{2}\pm 2\sqrt{2}}{\sqrt{3}}$

$x=\frac{\sqrt{2}+2\sqrt{2}}{\sqrt{3}}=\frac{\sqrt{2}}{\sqrt{3}}$

Or $x=\frac{\sqrt{2}-2\sqrt{2}}{\sqrt{3}}=-\frac{\sqrt{2}}{\sqrt{3}}$