To solve the equation, we need the equation in the form $a x^{2}+b x+c=0$. $x^{2}-9 x+14=0$ is already in this form.

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 $x^{2}-9 x+14=0$. By remembering the form $a x^{2}+b x+c=0$ :

$\mathrm{a}=1, \mathrm{~b}=-9, \mathrm{c}=14$

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

$\Delta=b^{2}-4 a c=(-9)^{2}-4 * 1 * 14=81-56=25$

$x_{1,2}=(-b \pm \sqrt{\Delta}) / 2 a=(-(-9) \pm \sqrt{25}) / 2=(9 \pm 5) / 2$

This means that the roots are, $x_{1}=(9-5) / 2=2$ and $x^{2}=(9+5) / 2=7$