21/n=3n+5

Solution for 21/n=3n+5 equation:

21/n=3n+5

We move all terms to the left:

21/n-(3n+5)=0


Domain of the equation: n!=0

n∈R


We get rid of parentheses

21/n-3n-5=0

We multiply all the terms by the denominator


-3n*n-5*n+21=0

We add all the numbers together, and all the variables

-5n-3n*n+21=0

Wy multiply elements

-3n^2-5n+21=0

a = -3; b = -5; c = +21;
Δ = b2-4ac
Δ = -52-4·(-3)·21
Δ = 277
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{-(-5)-\sqrt{277}}{2*-3}=\frac{5-\sqrt{277}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{277}}{2*-3}=\frac{5+\sqrt{277}}{-6}
$