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

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

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

We move all terms to the left:

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


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

4(-3n+2)n

We multiply parentheses

-12n^2+8n

Back to the equation:

-(-12n^2+8n)


We get rid of parentheses

12n^2-8n-4n-8=0

We add all the numbers together, and all the variables

12n^2-12n-8=0

a = 12; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·12·(-8)
Δ = 528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{33}}{2*12}=\frac{12-4\sqrt{33}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{33}}{2*12}=\frac{12+4\sqrt{33}}{24}
$