(10000)2=(800x)2+(600x)2

Solution for (10000)2=(800x)2+(600x)2 equation:

(10000)2=(800x)2+(600x)2

We move all terms to the left:

(10000)2-((800x)2+(600x)2)=0

We add all the numbers together, and all the variables

-(+1400x^2)+100002=0

We get rid of parentheses

-1400x^2+100002=0

a = -1400; b = 0; c = +100002;
Δ = b2-4ac
Δ = 02-4·(-1400)·100002
Δ = 560011200
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:

$\sqrt{\Delta}=\sqrt{560011200}=\sqrt{78400*7143}=\sqrt{78400}*\sqrt{7143}=280\sqrt{7143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-280\sqrt{7143}}{2*-1400}=\frac{0-280\sqrt{7143}}{-2800}
=-\frac{280\sqrt{7143}}{-2800}
=-\frac{\sqrt{7143}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+280\sqrt{7143}}{2*-1400}=\frac{0+280\sqrt{7143}}{-2800}
=\frac{280\sqrt{7143}}{-2800}
=\frac{\sqrt{7143}}{-10}
$