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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(-2n+4n(n-3)), so:

-2n+4n(n-3)

We multiply parentheses

4n^2-2n-12n

We add all the numbers together, and all the variables

4n^2-14n

Back to the equation:

-(4n^2-14n)


We get rid of parentheses

-4n^2+14n-6=0

a = -4; b = 14; c = -6;
Δ = b2-4ac
Δ = 142-4·(-4)·(-6)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*-4}=\frac{-24}{-8}
=+3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-4}=\frac{-4}{-8}
=1/2
$