To solve the equation, first we need to arrange it to appear in the form ax2 + bx $+c=0$ by removing the denominator:

$\mathrm{x}-31 / \mathrm{x}=0 \ldots$ First, we enlarge the equation by $\mathrm{x}$ :

$x^{\star} x-31 * x / x=0$

$x^{2}-31=0$

The quadratic formula to find the roots of a quadratic equation is:

$\mathrm{x}_{1,2}=(-\mathrm{b} \pm \sqrt{\Delta}) / 2 \mathrm{a}$ where $\Delta=\mathrm{b}^{2}-4 \mathrm{ac}$ and is called the discriminant of the quadratic equation.

In our question, the equation is $x^{2}-31=0$. By remembering the form $a x^{2}+b x+c=0$ :

$a=1, b=0, c=-31$

So, we can find the discriminant first, and then the roots of the equation:

$\Delta=b^{2}-4 a c=02-4 * 1 *(-31)=124$

$x_{1,2}=(-b \pm \sqrt{\Delta}) / 2 a=(\pm \sqrt{124}) / 2=(\pm \sqrt{4} \star 31) / 2$

$=(\pm 2 \sqrt{3} 1) / 2 \ldots$ Simplifying by 2 :

$x_{1,2}=\pm \sqrt{3} 1 \ldots$ This means that the roots are $\sqrt{31}$ and $-\sqrt{31}$.