# How do you solve 6x²-81=0?

May 23, 2015

We can manipulate the expression by isolating $x$. Alternatively, we can proceed to use Bhaskara.

Isolating $x$

$6 {x}^{2} - 81 = 0$
${x}^{2} = \frac{81}{6}$
$x = \sqrt{\frac{81}{6}}$
$x = \pm \frac{9}{\sqrt{6}}$
Rationalizing:
$x = \pm \frac{3 \sqrt{6}}{6}$

Using Bhaskara, where $a = 6$, $b = 0$ and $c = - 81$

$\frac{- 0 \pm \sqrt{0 - 4 \left(6\right) \left(- 81\right)}}{12}$
$\frac{\pm \sqrt{1944}}{12}$
$\frac{\pm \sqrt{{2}^{3} \cdot {3}^{5}}}{12}$
$\frac{\pm 18 \sqrt{6}}{12}$

$\pm \frac{3 \sqrt{6}}{2}$

P.s.: there are other forms, but these seem so simple they appeal to me!