Question

Find the roots of the following quadratic equations, if they exist
$4x^2+4\sqrt{3}x+3=0$

Answer 1

$4x^2+4\sqrt{3}x+3=0$

$x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$a=4,b=4\sqrt{3},c=3$

$x_{1,2}=\frac{-4\sqrt{3}\pm \sqrt{(-4\sqrt{3}{)}^2-4(4\left)\right(3)}}{2\cdot 4}$

$x=\frac{-4\sqrt{3}}{2\cdot 4}$

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