3(n+3)=2n(3-1)

Solution for 3(n+3)=2n(3-1) equation:

3(n+3)=2n(3-1)

We move all terms to the left:

3(n+3)-(2n(3-1))=0

We add all the numbers together, and all the variables

3(n+3)-(2n2)=0

We add all the numbers together, and all the variables

-2n^2+3(n+3)=0

We multiply parentheses

-2n^2+3n+9=0

a = -2; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-2)·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-2}=\frac{-12}{-4}
=+3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-2}=\frac{6}{-4}
=-1+1/2
$