100=500-5x^2

Solution for 100=500-5x^2 equation:

100=500-5x^2

We move all terms to the left:

100-(500-5x^2)=0

We get rid of parentheses

5x^2-500+100=0

We add all the numbers together, and all the variables

5x^2-400=0

a = 5; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·5·(-400)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*5}=\frac{0-40\sqrt{5}}{10}
=-\frac{40\sqrt{5}}{10}
=-4\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*5}=\frac{0+40\sqrt{5}}{10}
=\frac{40\sqrt{5}}{10}
=4\sqrt{5}
$