3(n-4)=-2(6-3/2n)

Solution for 3(n-4)=-2(6-3/2n) equation:

3(n-4)=-2(6-3/2n)

We move all terms to the left:

3(n-4)-(-2(6-3/2n))=0


Domain of the equation: 2n))!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3(n-4)-(-2(-3/2n+6))=0

We multiply parentheses

3n-(-2(-3/2n+6))-12=0

We multiply all the terms by the denominator


3n*2n-12*2n-3+6))-(-2(+6))=0

We add all the numbers together, and all the variables

3n*2n-12*2n-3+6))-(-26)=0

We add all the numbers together, and all the variables

3n*2n-12*2n=0

Wy multiply elements

6n^2-24n=0

a = 6; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·6·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*6}=\frac{0}{12}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*6}=\frac{48}{12}
=4
$