0=12x^2-250x+819

Solution for 0=12x^2-250x+819 equation:

0=12x^2-250x+819

We move all terms to the left:

0-(12x^2-250x+819)=0

We add all the numbers together, and all the variables

-(12x^2-250x+819)=0

We get rid of parentheses

-12x^2+250x-819=0

a = -12; b = 250; c = -819;
Δ = b2-4ac
Δ = 2502-4·(-12)·(-819)
Δ = 23188
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:

$\sqrt{\Delta}=\sqrt{23188}=\sqrt{4*5797}=\sqrt{4}*\sqrt{5797}=2\sqrt{5797}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-2\sqrt{5797}}{2*-12}=\frac{-250-2\sqrt{5797}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+2\sqrt{5797}}{2*-12}=\frac{-250+2\sqrt{5797}}{-24}
$