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2n-1/3n=24

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Solution for 2n-1/3n=24 equation:



2n-1/3n=24
We move all terms to the left:
2n-1/3n-(24)=0
Domain of the equation: 3n!=0
n!=0/3
n!=0
n∈R
We multiply all the terms by the denominator
2n*3n-24*3n-1=0
Wy multiply elements
6n^2-72n-1=0
a = 6; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·6·(-1)
Δ = 5208
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{5208}=\sqrt{4*1302}=\sqrt{4}*\sqrt{1302}=2\sqrt{1302}
n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1302}}{2*6}=\frac{72-2\sqrt{1302}}{12}
n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1302}}{2*6}=\frac{72+2\sqrt{1302}}{12}

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