Answer
$x=-\sqrt{3}+2i$ or $x=-\sqrt{3}-2i$
Work Step by Step
$\sqrt{3}x^2+6x+7\sqrt{3}=0$
Solve by using the quadratic formula:
^$x=\frac{−b±\sqrt{b^2−4ac}}{2a}$
$a=\sqrt{3}$, $b=6$, $c=7\sqrt{3}$
$x=\frac{−6±\sqrt{(6)^2−(4⋅\sqrt{3}⋅7\sqrt{3})}}{2⋅\sqrt{3}}$
$x=\frac{−6±\sqrt{36−(84)}}{2\sqrt{3}}$
$x=\frac{−6±\sqrt{-48}}{2\sqrt{3}}$
$x=\frac{−6±4\sqrt{-3}⋅\sqrt{-1}}{2\sqrt{3}}$
$x=\frac{−6±4\sqrt{3}i}{2\sqrt{3}}$
$x=\frac{−6+4\sqrt{3}i}{2\sqrt{3}}$ or $x=\frac{−6-4\sqrt{3}i}{2\sqrt{3}}$
$x=\frac{2(−3+2\sqrt{3}i)}{2\sqrt{3}}$ or $x=\frac{2(−3-2\sqrt{3}i)}{2\sqrt{3}}$
$x=\frac{−3+2\sqrt{3}i}{\sqrt{3}}$ or $x=\frac{−3-2\sqrt{3}i}{\sqrt{3}}$
$x=\frac{\sqrt{3}(−\sqrt{3}+2i)}{\sqrt{3}}$ or $x=\frac{\sqrt{3}(−\sqrt{3}-2i)}{\sqrt{3}}$
$x=-\sqrt{3}+2i$ or $x=-\sqrt{3}-2i$
