11-2/3n=n+4

Solution for 11-2/3n=n+4 equation:

11-2/3n=n+4

We move all terms to the left:

11-2/3n-(n+4)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

-2/3n-n-4+11=0

We multiply all the terms by the denominator


-n*3n-4*3n+11*3n-2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -3; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·(-3)·(-2)
Δ = 417
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{-(21)-\sqrt{417}}{2*-3}=\frac{-21-\sqrt{417}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{417}}{2*-3}=\frac{-21+\sqrt{417}}{-6}
$