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2x^2+500x-40000=0
a = 2; b = 500; c = -40000;
Δ = b2-4ac
Δ = 5002-4·2·(-40000)
Δ = 570000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{570000}=\sqrt{10000*57}=\sqrt{10000}*\sqrt{57}=100\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-100\sqrt{57}}{2*2}=\frac{-500-100\sqrt{57}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+100\sqrt{57}}{2*2}=\frac{-500+100\sqrt{57}}{4} $
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