13400=480-2x-1000+2x^2

Solution for 13400=480-2x-1000+2x^2 equation:

13400=480-2x-1000+2x^2

We move all terms to the left:

13400-(480-2x-1000+2x^2)=0

We get rid of parentheses

-2x^2+2x-480+1000+13400=0

We add all the numbers together, and all the variables

-2x^2+2x+13920=0

a = -2; b = 2; c = +13920;
Δ = b2-4ac
Δ = 22-4·(-2)·13920
Δ = 111364
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:

$\sqrt{\Delta}=\sqrt{111364}=\sqrt{4*27841}=\sqrt{4}*\sqrt{27841}=2\sqrt{27841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{27841}}{2*-2}=\frac{-2-2\sqrt{27841}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{27841}}{2*-2}=\frac{-2+2\sqrt{27841}}{-4}
$