0=12x^2-240x+819

Solution for 0=12x^2-240x+819 equation:

0=12x^2-240x+819

We move all terms to the left:

0-(12x^2-240x+819)=0

We add all the numbers together, and all the variables

-(12x^2-240x+819)=0

We get rid of parentheses

-12x^2+240x-819=0

a = -12; b = 240; c = -819;
Δ = b2-4ac
Δ = 2402-4·(-12)·(-819)
Δ = 18288
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:

$\sqrt{\Delta}=\sqrt{18288}=\sqrt{144*127}=\sqrt{144}*\sqrt{127}=12\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-12\sqrt{127}}{2*-12}=\frac{-240-12\sqrt{127}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+12\sqrt{127}}{2*-12}=\frac{-240+12\sqrt{127}}{-24}
$