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n-1/2n=36

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Solution for n-1/2n=36 equation:



n-1/2n=36
We move all terms to the left:
n-1/2n-(36)=0
Domain of the equation: 2n!=0
n!=0/2
n!=0
n∈R
We multiply all the terms by the denominator
n*2n-36*2n-1=0
Wy multiply elements
2n^2-72n-1=0
a = 2; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·2·(-1)
Δ = 5192
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{5192}=\sqrt{4*1298}=\sqrt{4}*\sqrt{1298}=2\sqrt{1298}
n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1298}}{2*2}=\frac{72-2\sqrt{1298}}{4}
n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1298}}{2*2}=\frac{72+2\sqrt{1298}}{4}

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