# How do you solve -5x^2 - 8x + 1 = 0 using the quadratic formula?

Aug 6, 2015

${x}_{1 , 2} = - \frac{4 \pm \sqrt{21}}{5}$

#### Explanation:

For the general form quadratic equation

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

the two solutions can be deterimed 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, you have $a = - 5$, $b = - 8$, and $c = 1$. The two solutions will take the form

${x}_{1 , 2} = \frac{- \left(- 8\right) \pm \sqrt{{\left(- 8\right)}^{2} - 4 \cdot \left(- 5\right) \cdot 1}}{2 \cdot \left(- 5\right)}$

${x}_{1 , 2} = \frac{8 \pm \sqrt{84}}{- 10} = - \frac{4 \pm \sqrt{21}}{5}$

This is equivalent to

${x}_{1} = \textcolor{g r e e n}{- \frac{4 + \sqrt{21}}{5}}$ and ${x}_{2} = \textcolor{g r e e n}{- \frac{4 - \sqrt{21}}{5}}$