4(n+7)=-44+2n(n+6)

Solution for 4(n+7)=-44+2n(n+6) equation:

4(n+7)=-44+2n(n+6)

We move all terms to the left:

4(n+7)-(-44+2n(n+6))=0

We multiply parentheses

4n-(-44+2n(n+6))+28=0


We calculate terms in parentheses: -(-44+2n(n+6)), so:

-44+2n(n+6)

determiningTheFunctionDomain
2n(n+6)-44

We multiply parentheses

2n^2+12n-44

Back to the equation:

-(2n^2+12n-44)


We get rid of parentheses

-2n^2+4n-12n+44+28=0

We add all the numbers together, and all the variables

-2n^2-8n+72=0

a = -2; b = -8; c = +72;
Δ = b2-4ac
Δ = -82-4·(-2)·72
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{10}}{2*-2}=\frac{8-8\sqrt{10}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{10}}{2*-2}=\frac{8+8\sqrt{10}}{-4}
$