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50000n^2+750000n=3200000
We move all terms to the left:
50000n^2+750000n-(3200000)=0
a = 50000; b = 750000; c = -3200000;
Δ = b2-4ac
Δ = 7500002-4·50000·(-3200000)
Δ = 1202500000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1202500000000}=\sqrt{2500000000*481}=\sqrt{2500000000}*\sqrt{481}=50000\sqrt{481}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(750000)-50000\sqrt{481}}{2*50000}=\frac{-750000-50000\sqrt{481}}{100000} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(750000)+50000\sqrt{481}}{2*50000}=\frac{-750000+50000\sqrt{481}}{100000} $
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