7n-4(n-8)=-8n(8-6n)

Solution for 7n-4(n-8)=-8n(8-6n) equation:

7n-4(n-8)=-8n(8-6n)

We move all terms to the left:

7n-4(n-8)-(-8n(8-6n))=0

We add all the numbers together, and all the variables

7n-4(n-8)-(-8n(-6n+8))=0

We multiply parentheses

7n-4n-(-8n(-6n+8))+32=0


We calculate terms in parentheses: -(-8n(-6n+8)), so:

-8n(-6n+8)

We multiply parentheses

48n^2-64n

Back to the equation:

-(48n^2-64n)


We add all the numbers together, and all the variables

3n-(48n^2-64n)+32=0

We get rid of parentheses

-48n^2+3n+64n+32=0

We add all the numbers together, and all the variables

-48n^2+67n+32=0

a = -48; b = 67; c = +32;
Δ = b2-4ac
Δ = 672-4·(-48)·32
Δ = 10633
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:

$\sqrt{\Delta}=\sqrt{10633}=\sqrt{49*217}=\sqrt{49}*\sqrt{217}=7\sqrt{217}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-7\sqrt{217}}{2*-48}=\frac{-67-7\sqrt{217}}{-96}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+7\sqrt{217}}{2*-48}=\frac{-67+7\sqrt{217}}{-96}
$