n=80;10000/n

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Solution for n=80;10000/n equation:



n=8010000/n
We move all terms to the left:
n-(8010000/n)=0
Domain of the equation: n)!=0
n!=0/1
n!=0
n∈R
We add all the numbers together, and all the variables
n-(+8010000/n)=0
We get rid of parentheses
n-8010000/n=0
We multiply all the terms by the denominator
n*n-8010000=0
Wy multiply elements
n^2-8010000=0
a = 1; b = 0; c = -8010000;
Δ = b2-4ac
Δ = 02-4·1·(-8010000)
Δ = 32040000
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:
$\sqrt{\Delta}=\sqrt{32040000}=\sqrt{360000*89}=\sqrt{360000}*\sqrt{89}=600\sqrt{89}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{89}}{2*1}=\frac{0-600\sqrt{89}}{2} =-\frac{600\sqrt{89}}{2} =-300\sqrt{89} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{89}}{2*1}=\frac{0+600\sqrt{89}}{2} =\frac{600\sqrt{89}}{2} =300\sqrt{89} $

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