4(n+16)=4n(n+16)+5

Solution for 4(n+16)=4n(n+16)+5 equation:

4(n+16)=4n(n+16)+5

We move all terms to the left:

4(n+16)-(4n(n+16)+5)=0

We multiply parentheses

4n-(4n(n+16)+5)+64=0


We calculate terms in parentheses: -(4n(n+16)+5), so:

4n(n+16)+5

We multiply parentheses

4n^2+64n+5

Back to the equation:

-(4n^2+64n+5)


We get rid of parentheses

-4n^2+4n-64n-5+64=0

We add all the numbers together, and all the variables

-4n^2-60n+59=0

a = -4; b = -60; c = +59;
Δ = b2-4ac
Δ = -602-4·(-4)·59
Δ = 4544
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:

$\sqrt{\Delta}=\sqrt{4544}=\sqrt{64*71}=\sqrt{64}*\sqrt{71}=8\sqrt{71}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{71}}{2*-4}=\frac{60-8\sqrt{71}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{71}}{2*-4}=\frac{60+8\sqrt{71}}{-8}
$