0=9x^2-54x-144

Solution for 0=9x^2-54x-144 equation:

0=9x^2-54x-144

We move all terms to the left:

0-(9x^2-54x-144)=0

We add all the numbers together, and all the variables

-(9x^2-54x-144)=0

We get rid of parentheses

-9x^2+54x+144=0

a = -9; b = 54; c = +144;
Δ = b2-4ac
Δ = 542-4·(-9)·144
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-90}{2*-9}=\frac{-144}{-18}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+90}{2*-9}=\frac{36}{-18}
=-2
$