320x^2+800-80x^2+200-320x^2=0

Solution for 320x^2+800-80x^2+200-320x^2=0 equation:

320x^2+800-80x^2+200-320x^2=0

We add all the numbers together, and all the variables

-80x^2+1000=0

a = -80; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-80)·1000
Δ = 320000
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:

$\sqrt{\Delta}=\sqrt{320000}=\sqrt{160000*2}=\sqrt{160000}*\sqrt{2}=400\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{2}}{2*-80}=\frac{0-400\sqrt{2}}{-160}
=-\frac{400\sqrt{2}}{-160}
=-\frac{5\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{2}}{2*-80}=\frac{0+400\sqrt{2}}{-160}
=\frac{400\sqrt{2}}{-160}
=\frac{5\sqrt{2}}{-2}
$