# How do you find all the real and complex roots of 18x²+3x-1=0?

Feb 1, 2016

here is how,

#### Explanation:

as $x$ has the highest power of $2$, there are two values of $x$

we know,

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

$= \frac{- 3 \pm \sqrt{{3}^{2} - 4 \cdot 18 \left(- 1\right)}}{2 \cdot 18}$

$= \frac{- 3 \pm \sqrt{9 + 72}}{36}$

$= \frac{- 3 \pm \sqrt{81}}{36}$

$= \frac{- 3 \pm 9}{36}$

using the + value,

$x = \frac{- 3 + 9}{36}$

$= \frac{6}{36}$

$= \frac{1}{6}$

using the - value,
$x = \frac{- 3 - 9}{36}$

$= - \frac{12}{36}$

$= - \frac{1}{3}$