-3n(n-4)=8-2n

Solution for -3n(n-4)=8-2n equation:

-3n(n-4)=8-2n

We move all terms to the left:

-3n(n-4)-(8-2n)=0

We add all the numbers together, and all the variables

-3n(n-4)-(-2n+8)=0

We multiply parentheses

-3n^2+12n-(-2n+8)=0

We get rid of parentheses

-3n^2+12n+2n-8=0

We add all the numbers together, and all the variables

-3n^2+14n-8=0

a = -3; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·(-3)·(-8)
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*-3}=\frac{-24}{-6}
=+4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-3}=\frac{-4}{-6}
=2/3
$