-8n+21=-1/3n

Solution for -8n+21=-1/3n equation:

-8n+21=-1/3n

We move all terms to the left:

-8n+21-(-1/3n)=0


Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We get rid of parentheses

-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}
$