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2000-2000x^2=x
We move all terms to the left:
2000-2000x^2-(x)=0
We add all the numbers together, and all the variables
-2000x^2-1x+2000=0
a = -2000; b = -1; c = +2000;
Δ = b2-4ac
Δ = -12-4·(-2000)·2000
Δ = 16000001
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{16000001}}{2*-2000}=\frac{1-\sqrt{16000001}}{-4000} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{16000001}}{2*-2000}=\frac{1+\sqrt{16000001}}{-4000} $
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