n^2+16n+64=25

Solution for n^2+16n+64=25 equation:

n^2+16n+64=25

We move all terms to the left:

n^2+16n+64-(25)=0

We add all the numbers together, and all the variables

n^2+16n+39=0

a = 1; b = 16; c = +39;
Δ = b2-4ac
Δ = 162-4·1·39
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-10}{2*1}=\frac{-26}{2}
=-13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+10}{2*1}=\frac{-6}{2}
=-3
$