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

Find the roots of the following quadratic equation if they exist:

$5x^2-7x-6=0$

Find the roots of the following quadratic equation if they exist:

$x^2-6x+5=0$

Find the roots of the quadratic equation by applying the quadratic formula:

$2x^2+x-4=0$

Find the roots of the quadratic equation by applying the quadratic formula:

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

Find the roots of the quadratic equation by applying the quadratic formula:

$5x^2-7x-6=0$

Find the roots of the quadratic equation applying the quadratic formula:

$x^2-6x+5=0$

Find the roots of the following equation:

$x-\frac{1}{x}=3, x\ne 0$

Find the roots of the following equation:

$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x\ne -4, 7$