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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(+1400x^2)+10000=0

We get rid of parentheses

-1400x^2+10000=0

a = -1400; b = 0; c = +10000;
Δ = b2-4ac
Δ = 02-4·(-1400)·10000
Δ = 56000000
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:

$\sqrt{\Delta}=\sqrt{56000000}=\sqrt{4000000*14}=\sqrt{4000000}*\sqrt{14}=2000\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{14}}{2*-1400}=\frac{0-2000\sqrt{14}}{-2800}
=-\frac{2000\sqrt{14}}{-2800}
=-\frac{5\sqrt{14}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{14}}{2*-1400}=\frac{0+2000\sqrt{14}}{-2800}
=\frac{2000\sqrt{14}}{-2800}
=\frac{5\sqrt{14}}{-7}
$