Solve the given two equations and select the correct answer from the given options.
$I.$ $5x^{2} + 2x - 3 = 0$
$II.$ $2y^{2} + 7y + 6 = 0$

Solve the given two equations and choose the correct option.
$I.$ $2x^2 - (4 + \sqrt{13})x + 2\sqrt{13} = 0$
$II.$ $10y^2 - (18 + 5\sqrt{13})y + 9\sqrt{13} = 0$

Solve the given two equations and select the correct option.
$I.$ $9x^{2} - 114x + 361 = 0$
$II.$ $y^{2} = 36$

$Quantity$ $1$: Height of the tank if the volume of a cylindrical tank is $12320 \, cm^3$. Its radius and height are in the ratio of $7:10$ respectively. $Quantity$ $2$: Height of the kerosene level in a jar if a cone of radius $2 \, cm$ and height $3 \, cm$ is melted and recast into a cylinder of radius $2 \, cm$.

If $\alpha, \beta$ are the roots of the equation $a x^{2}+b x+b=0,$ then $\sqrt{\frac{\alpha}{\beta}}+\sqrt{\frac{\beta}{\alpha}}+\sqrt{\frac{b}{a}}=$

Find the value of $x^{3}+y^{3}+z^{3}-3xyz$ when $x=89, y=87, z=84$.