# How do you solve x^2-3x>54 using a sign chart?

##### 1 Answer
Jan 19, 2017

The answer is  x in ] -oo,-6 [ uu ] 9, oo [

#### Explanation:

Let's rewrite the inequality

${x}^{2} - 3 x - 54 > 0$

Let's factorise

${x}^{2} - 3 x - 54 = \left(x + 6\right) \left(x - 9\right)$

and let $f \left(x\right) = {x}^{2} - 3 x - 54$

Now we can make the sign chart

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a}$$- 6$$\textcolor{w h i t e}{a a a a}$$9$$\textcolor{w h i t e}{a a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x + 6$$\textcolor{w h i t e}{a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$x - 9$$\textcolor{w h i t e}{a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$f \left(x\right)$$\textcolor{w h i t e}{a a a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

Therefore,

$f \left(x\right) > 0$, when  x in ] -oo,-6 [ uu ] 9, oo [