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-8n+21=-1/3n
We move all terms to the left:
-8n+21-(-1/3n)=0
Domain of the equation: 3n)!=0We get rid of parentheses
n!=0/1
n!=0
n∈R
-8n+1/3n+21=0
We multiply all the terms by the denominator
-8n*3n+21*3n+1=0
Wy multiply elements
-24n^2+63n+1=0
a = -24; b = 63; c = +1;
Δ = b2-4ac
Δ = 632-4·(-24)·1
Δ = 4065
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-\sqrt{4065}}{2*-24}=\frac{-63-\sqrt{4065}}{-48} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+\sqrt{4065}}{2*-24}=\frac{-63+\sqrt{4065}}{-48} $
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