How do you solve using the quadratic formula 5x^2-8x-14=0?

1 Answer
May 10, 2015

$5 {x}^{2} - 8 x - 14 = 0$ is of the form $a {x}^{2} + b x + c = 0$, with $a = 5$, $b = - 8$ and $c = - 14$.

The quadratic formula gives $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

So substituting our values for $a$, $b$ and $c$, we get:

$x = \frac{8 \pm \sqrt{{8}^{2} - 4 \cdot 5 \cdot \left(- 14\right)}}{2 \cdot 5}$

$= \frac{8 \pm \sqrt{4 \cdot 16 + 4 \cdot 70}}{10}$

$= \frac{8 \pm \sqrt{4 \cdot 86}}{10}$

$= \frac{8 \pm \sqrt{4} \cdot \sqrt{86}}{10}$

$= \frac{8 \pm 2 \cdot \sqrt{86}}{10}$

$= \frac{4 \pm \sqrt{86}}{5}$

$= \frac{4}{5} \pm \frac{\sqrt{86}}{5}$