21/2n=3n+16

Solution for 21/2n=3n+16 equation:

21/2n=3n+16

We move all terms to the left:

21/2n-(3n+16)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

21/2n-3n-16=0

We multiply all the terms by the denominator


-3n*2n-16*2n+21=0

Wy multiply elements

-6n^2-32n+21=0

a = -6; b = -32; c = +21;
Δ = b2-4ac
Δ = -322-4·(-6)·21
Δ = 1528
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:

$\sqrt{\Delta}=\sqrt{1528}=\sqrt{4*382}=\sqrt{4}*\sqrt{382}=2\sqrt{382}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{382}}{2*-6}=\frac{32-2\sqrt{382}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{382}}{2*-6}=\frac{32+2\sqrt{382}}{-12}
$