1/3n-11=n+4

Solution for 1/3n-11=n+4 equation:

1/3n-11=n+4

We move all terms to the left:

1/3n-11-(n+4)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

1/3n-n-4-11=0

We multiply all the terms by the denominator


-n*3n-4*3n-11*3n+1=0

Wy multiply elements

-3n^2-12n-33n+1=0

We add all the numbers together, and all the variables

-3n^2-45n+1=0

a = -3; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·(-3)·1
Δ = 2037
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{-(-45)-\sqrt{2037}}{2*-3}=\frac{45-\sqrt{2037}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2037}}{2*-3}=\frac{45+\sqrt{2037}}{-6}
$