# How do you solve (sqrt2)x² - x - 3(sqrt2) =0?

Aug 31, 2015

${x}_{1 , 2} = \frac{1 \pm 5}{2 \sqrt{2}}$

#### Explanation:

You know that for a general form quadratic equation

$\textcolor{b l u e}{a {x}^{2} + b x + c = 0}$

you can find its roots by using the quadratic formula

$\textcolor{b l u e}{{x}_{1 , 2} = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}}$

In your case, $a = \sqrt{2}$, $b = - 1$, and $c = - 3 \sqrt{2}$. This means that you have

${x}_{1 , 2} = \frac{\left(- 1\right) \pm \sqrt{{\left(- 1\right)}^{2} - 4 \cdot \sqrt{2} \cdot \left(- 3 \sqrt{2}\right)}}{2 \cdot \sqrt{2}}$

${x}_{1 , 2} = \frac{1 \pm \sqrt{1 + 12 \cdot 2}}{2 \sqrt{2}}$

${x}_{1 , 2} = \frac{1 \pm 5}{2 \sqrt{2}}$

The two solutions to this equation will be

${x}_{1} = \frac{1 + 5}{2 \sqrt{2}} = \textcolor{g r e e n}{\frac{3 \sqrt{2}}{2}} \text{ }$ and $\text{ } {x}_{2} = \frac{1 - 5}{2 \sqrt{2}} = \textcolor{g r e e n}{- \sqrt{2}}$