x^2=10000-100x

Solution for x^2=10000-100x equation:

x^2=10000-100x

We move all terms to the left:

x^2-(10000-100x)=0

We add all the numbers together, and all the variables

x^2-(-100x+10000)=0

We get rid of parentheses

x^2+100x-10000=0

a = 1; b = 100; c = -10000;
Δ = b2-4ac
Δ = 1002-4·1·(-10000)
Δ = 50000
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:

$\sqrt{\Delta}=\sqrt{50000}=\sqrt{10000*5}=\sqrt{10000}*\sqrt{5}=100\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{5}}{2*1}=\frac{-100-100\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{5}}{2*1}=\frac{-100+100\sqrt{5}}{2}
$