5x^2=10000+x^2

Solution for 5x^2=10000+x^2 equation:

5x^2=10000+x^2

We move all terms to the left:

5x^2-(10000+x^2)=0

We get rid of parentheses

5x^2-x^2-10000=0

We add all the numbers together, and all the variables

4x^2-10000=0

a = 4; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·4·(-10000)
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400}{2*4}=\frac{-400}{8}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400}{2*4}=\frac{400}{8}
=50
$