x^2+8x+16-16(x+4)+63=0

Solution for x^2+8x+16-16(x+4)+63=0 equation:

x^2+8x+16-16(x+4)+63=0

We add all the numbers together, and all the variables

x^2+8x-16(x+4)+79=0

We multiply parentheses

x^2+8x-16x-64+79=0

We add all the numbers together, and all the variables

x^2-8x+15=0

a = 1; b = -8; c = +15;
Δ = b2-4ac
Δ = -82-4·1·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*1}=\frac{10}{2}
=5
$