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10n^2=840
We move all terms to the left:
10n^2-(840)=0
a = 10; b = 0; c = -840;
Δ = b2-4ac
Δ = 02-4·10·(-840)
Δ = 33600
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{33600}=\sqrt{1600*21}=\sqrt{1600}*\sqrt{21}=40\sqrt{21}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{21}}{2*10}=\frac{0-40\sqrt{21}}{20} =-\frac{40\sqrt{21}}{20} =-2\sqrt{21} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{21}}{2*10}=\frac{0+40\sqrt{21}}{20} =\frac{40\sqrt{21}}{20} =2\sqrt{21} $
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