12000=2x^2+853x-12000

Solution for 12000=2x^2+853x-12000 equation:

12000=2x^2+853x-12000

We move all terms to the left:

12000-(2x^2+853x-12000)=0

We get rid of parentheses

-2x^2-853x+12000+12000=0

We add all the numbers together, and all the variables

-2x^2-853x+24000=0

a = -2; b = -853; c = +24000;
Δ = b2-4ac
Δ = -8532-4·(-2)·24000
Δ = 919609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-853)-\sqrt{919609}}{2*-2}=\frac{853-\sqrt{919609}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-853)+\sqrt{919609}}{2*-2}=\frac{853+\sqrt{919609}}{-4}
$