0=12x^2-54x-180

Solution for 0=12x^2-54x-180 equation:

0=12x^2-54x-180

We move all terms to the left:

0-(12x^2-54x-180)=0

We add all the numbers together, and all the variables

-(12x^2-54x-180)=0

We get rid of parentheses

-12x^2+54x+180=0

a = -12; b = 54; c = +180;
Δ = b2-4ac
Δ = 542-4·(-12)·180
Δ = 11556
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11556}=\sqrt{36*321}=\sqrt{36}*\sqrt{321}=6\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{321}}{2*-12}=\frac{-54-6\sqrt{321}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{321}}{2*-12}=\frac{-54+6\sqrt{321}}{-24}
$