# How do you solve the equation x^2-3x-2=0 using the quadratic formula?

Oct 31, 2016

$x = \frac{3}{2} \pm \frac{\sqrt{17}}{2}$

#### Explanation:

${x}^{2} - 3 x - 2 = 0$

is in the form:

$a {x}^{2} + b x + c = 0$

with $a = 1$, $b = - 3$ and $c = - 2$

We can use the quadratic formula to find the roots:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$\textcolor{w h i t e}{x} = \frac{- \left(\textcolor{b l u e}{- 3}\right) \pm \sqrt{{\left(\textcolor{b l u e}{- 3}\right)}^{2} - 4 \left(\textcolor{b l u e}{1}\right) \left(\textcolor{b l u e}{- 2}\right)}}{2 \left(\textcolor{b l u e}{1}\right)}$

$\textcolor{w h i t e}{x} = \frac{3 \pm \sqrt{9 + 8}}{2}$

$\textcolor{w h i t e}{x} = \frac{3}{2} \pm \frac{\sqrt{17}}{2}$