Question:

Find the solution of the quadratic equation $3 \sqrt{3} x^{2}+10 x+\sqrt{3}=0$.

Solution:

The given quadratic equation is $3 \sqrt{3} x^{2}+10 x+\sqrt{3}=0$.

$3 \sqrt{3} x^{2}+10 x+\sqrt{3}=0$

$\Rightarrow 3 \sqrt{3} x^{2}+9 x+x+\sqrt{3}=0$

$\Rightarrow 3 \sqrt{3} x(x+\sqrt{3})+1(x+\sqrt{3})=0$

$\Rightarrow(x+\sqrt{3})(3 \sqrt{3} x+1)=0$

$\Rightarrow x+\sqrt{3}=0$ or $3 \sqrt{3} x+1=0$

$\Rightarrow x=-\sqrt{3}$ or $x=-\frac{1}{3 \sqrt{3}}=-\frac{\sqrt{3}}{9}$

Hence, $-\sqrt{3}$ and $-\frac{\sqrt{3}}{9}$ are the solutions of the given equation.