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4/2=n-10/n

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Solution for 4/2=n-10/n equation:



4/2=n-10/n
We move all terms to the left:
4/2-(n-10/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-10/n)+4/2=0
We add all the numbers together, and all the variables
-(+n-10/n)+2=0
We get rid of parentheses
-n+10/n+2=0
We multiply all the terms by the denominator
-n*n+2*n+10=0
We add all the numbers together, and all the variables
2n-n*n+10=0
Wy multiply elements
-1n^2+2n+10=0
a = -1; b = 2; c = +10;
Δ = b2-4ac
Δ = 22-4·(-1)·10
Δ = 44
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{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}
n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{11}}{2*-1}=\frac{-2-2\sqrt{11}}{-2}
n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{11}}{2*-1}=\frac{-2+2\sqrt{11}}{-2}

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