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

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

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

We move all terms to the left:

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


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

-3n(4n-4)

We multiply parentheses

-12n^2+12n

Back to the equation:

-(-12n^2+12n)


We get rid of parentheses

12n^2-12n-2n+2=0

We add all the numbers together, and all the variables

12n^2-14n+2=0

a = 12; b = -14; c = +2;
Δ = b2-4ac
Δ = -142-4·12·2
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*12}=\frac{4}{24}
=1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*12}=\frac{24}{24}
=1
$