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500x^2-1000=0
a = 500; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·500·(-1000)
Δ = 2000000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2000000}=\sqrt{1000000*2}=\sqrt{1000000}*\sqrt{2}=1000\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000\sqrt{2}}{2*500}=\frac{0-1000\sqrt{2}}{1000} =-\frac{1000\sqrt{2}}{1000} =-\sqrt{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000\sqrt{2}}{2*500}=\frac{0+1000\sqrt{2}}{1000} =\frac{1000\sqrt{2}}{1000} =\sqrt{2} $
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