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500x^2=100
We move all terms to the left:
500x^2-(100)=0
a = 500; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·500·(-100)
Δ = 200000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{200000}=\sqrt{40000*5}=\sqrt{40000}*\sqrt{5}=200\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{5}}{2*500}=\frac{0-200\sqrt{5}}{1000} =-\frac{200\sqrt{5}}{1000} =-\frac{\sqrt{5}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{5}}{2*500}=\frac{0+200\sqrt{5}}{1000} =\frac{200\sqrt{5}}{1000} =\frac{\sqrt{5}}{5} $
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