0=x^2-64x-192

Solution for 0=x^2-64x-192 equation:

0=x^2-64x-192

We move all terms to the left:

0-(x^2-64x-192)=0

We add all the numbers together, and all the variables

-(x^2-64x-192)=0

We get rid of parentheses

-x^2+64x+192=0

We add all the numbers together, and all the variables

-1x^2+64x+192=0

a = -1; b = 64; c = +192;
Δ = b2-4ac
Δ = 642-4·(-1)·192
Δ = 4864
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:

$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-16\sqrt{19}}{2*-1}=\frac{-64-16\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+16\sqrt{19}}{2*-1}=\frac{-64+16\sqrt{19}}{-2}
$