-x^2+128x-256=0

Solution for -x^2+128x-256=0 equation:

-x^2+128x-256=0

We add all the numbers together, and all the variables

-1x^2+128x-256=0

a = -1; b = 128; c = -256;
Δ = b2-4ac
Δ = 1282-4·(-1)·(-256)
Δ = 15360
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:

$\sqrt{\Delta}=\sqrt{15360}=\sqrt{1024*15}=\sqrt{1024}*\sqrt{15}=32\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-32\sqrt{15}}{2*-1}=\frac{-128-32\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+32\sqrt{15}}{2*-1}=\frac{-128+32\sqrt{15}}{-2}
$