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-0.5x^2+200x-2000=0
a = -0.5; b = 200; c = -2000;
Δ = b2-4ac
Δ = 2002-4·(-0.5)·(-2000)
Δ = 36000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36000}=\sqrt{3600*10}=\sqrt{3600}*\sqrt{10}=60\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-60\sqrt{10}}{2*-0.5}=\frac{-200-60\sqrt{10}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+60\sqrt{10}}{2*-0.5}=\frac{-200+60\sqrt{10}}{-1} $
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