2n+2/1n=10

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Solution for 2n+2/1n=10 equation:



2n+2/1n=10
We move all terms to the left:
2n+2/1n-(10)=0
Domain of the equation: 1n!=0
n∈R
We multiply all the terms by the denominator
2n*1n-10*1n+2=0
Wy multiply elements
2n^2-10n+2=0
a = 2; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·2·2
Δ = 84
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:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*2}=\frac{10-2\sqrt{21}}{4} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*2}=\frac{10+2\sqrt{21}}{4} $

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