1/3n-n=5

Solution for 1/3n-n=5 equation:

1/3n-n=5

We move all terms to the left:

1/3n-n-(5)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+1/3n-5=0

We multiply all the terms by the denominator


-1n*3n-5*3n+1=0

Wy multiply elements

-3n^2-15n+1=0

a = -3; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-3)·1
Δ = 237
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{-(-15)-\sqrt{237}}{2*-3}=\frac{15-\sqrt{237}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{237}}{2*-3}=\frac{15+\sqrt{237}}{-6}
$