-6n+6=3n(n-1)

Solution for -6n+6=3n(n-1) equation:

-6n+6=3n(n-1)

We move all terms to the left:

-6n+6-(3n(n-1))=0


We calculate terms in parentheses: -(3n(n-1)), so:

3n(n-1)

We multiply parentheses

3n^2-3n

Back to the equation:

-(3n^2-3n)


We get rid of parentheses

-3n^2-6n+3n+6=0

We add all the numbers together, and all the variables

-3n^2-3n+6=0

a = -3; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-3)·6
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*-3}=\frac{-6}{-6}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*-3}=\frac{12}{-6}
=-2
$