400-2x^2=x

Solution for 400-2x^2=x equation:

400-2x^2=x

We move all terms to the left:

400-2x^2-(x)=0

We add all the numbers together, and all the variables

-2x^2-1x+400=0

a = -2; b = -1; c = +400;
Δ = b2-4ac
Δ = -12-4·(-2)·400
Δ = 3201
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{-(-1)-\sqrt{3201}}{2*-2}=\frac{1-\sqrt{3201}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{3201}}{2*-2}=\frac{1+\sqrt{3201}}{-4}
$