0=x^2+16x-64

Solution for 0=x^2+16x-64 equation:

0=x^2+16x-64

We move all terms to the left:

0-(x^2+16x-64)=0

We add all the numbers together, and all the variables

-(x^2+16x-64)=0

We get rid of parentheses

-x^2-16x+64=0

We add all the numbers together, and all the variables

-1x^2-16x+64=0

a = -1; b = -16; c = +64;
Δ = b2-4ac
Δ = -162-4·(-1)·64
Δ = 512
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{2}}{2*-1}=\frac{16-16\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{2}}{2*-1}=\frac{16+16\sqrt{2}}{-2}
$