-44+-4/3n=12+n

Solution for -44+-4/3n=12+n equation:

-44+-4/3n=12+n

We move all terms to the left:

-44+-4/3n-(12+n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-4/3n-(n+12)-44+=0

We add all the numbers together, and all the variables

-4/3n-(n+12)=0

We get rid of parentheses

-4/3n-n-12=0

We multiply all the terms by the denominator


-n*3n-12*3n-4=0

Wy multiply elements

-3n^2-36n-4=0

a = -3; b = -36; c = -4;
Δ = b2-4ac
Δ = -362-4·(-3)·(-4)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{78}}{2*-3}=\frac{36-4\sqrt{78}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{78}}{2*-3}=\frac{36+4\sqrt{78}}{-6}
$