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n-2*180/n=156
We move all terms to the left:
n-2*180/n-(156)=0
Domain of the equation: n!=0We multiply all the terms by the denominator
n∈R
n*n-156*n-2*180=0
We add all the numbers together, and all the variables
-156n+n*n-360=0
Wy multiply elements
n^2-156n-360=0
a = 1; b = -156; c = -360;
Δ = b2-4ac
Δ = -1562-4·1·(-360)
Δ = 25776
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25776}=\sqrt{144*179}=\sqrt{144}*\sqrt{179}=12\sqrt{179}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-12\sqrt{179}}{2*1}=\frac{156-12\sqrt{179}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+12\sqrt{179}}{2*1}=\frac{156+12\sqrt{179}}{2} $
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