x^2-128x-1600=0

Solution for x^2-128x-1600=0 equation:

x^2-128x-1600=0

a = 1; b = -128; c = -1600;
Δ = b2-4ac
Δ = -1282-4·1·(-1600)
Δ = 22784
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:

$\sqrt{\Delta}=\sqrt{22784}=\sqrt{256*89}=\sqrt{256}*\sqrt{89}=16\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-16\sqrt{89}}{2*1}=\frac{128-16\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+16\sqrt{89}}{2*1}=\frac{128+16\sqrt{89}}{2}
$