100x=2500-x^2

Solution for 100x=2500-x^2 equation:

100x=2500-x^2

We move all terms to the left:

100x-(2500-x^2)=0

We get rid of parentheses

x^2+100x-2500=0

a = 1; b = 100; c = -2500;
Δ = b2-4ac
Δ = 1002-4·1·(-2500)
Δ = 20000
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:

$\sqrt{\Delta}=\sqrt{20000}=\sqrt{10000*2}=\sqrt{10000}*\sqrt{2}=100\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{2}}{2*1}=\frac{-100-100\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{2}}{2*1}=\frac{-100+100\sqrt{2}}{2}
$