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

-(800x^2+600x^2)+100000000=0

We get rid of parentheses

-800x^2-600x^2+100000000=0

We add all the numbers together, and all the variables

-1400x^2+100000000=0

a = -1400; b = 0; c = +100000000;
Δ = b2-4ac
Δ = 02-4·(-1400)·100000000
Δ = 560000000000
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:

$\sqrt{\Delta}=\sqrt{560000000000}=\sqrt{40000000000*14}=\sqrt{40000000000}*\sqrt{14}=200000\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200000\sqrt{14}}{2*-1400}=\frac{0-200000\sqrt{14}}{-2800}
=-\frac{200000\sqrt{14}}{-2800}
=-\frac{500\sqrt{14}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200000\sqrt{14}}{2*-1400}=\frac{0+200000\sqrt{14}}{-2800}
=\frac{200000\sqrt{14}}{-2800}
=\frac{500\sqrt{14}}{-7}
$