6-(4-4n)+17n=-6+18n(n+1)

Solution for 6-(4-4n)+17n=-6+18n(n+1) equation:

6-(4-4n)+17n=-6+18n(n+1)

We move all terms to the left:

6-(4-4n)+17n-(-6+18n(n+1))=0

We add all the numbers together, and all the variables

-(-4n+4)+17n-(-6+18n(n+1))+6=0

We add all the numbers together, and all the variables

17n-(-4n+4)-(-6+18n(n+1))+6=0

We get rid of parentheses

17n+4n-(-6+18n(n+1))-4+6=0


We calculate terms in parentheses: -(-6+18n(n+1)), so:

-6+18n(n+1)

determiningTheFunctionDomain
18n(n+1)-6

We multiply parentheses

18n^2+18n-6

Back to the equation:

-(18n^2+18n-6)


We add all the numbers together, and all the variables

21n-(18n^2+18n-6)+2=0

We get rid of parentheses

-18n^2+21n-18n+6+2=0

We add all the numbers together, and all the variables

-18n^2+3n+8=0

a = -18; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-18)·8
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{65}}{2*-18}=\frac{-3-3\sqrt{65}}{-36}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{65}}{2*-18}=\frac{-3+3\sqrt{65}}{-36}
$