x^2-4096x-16384=0

Solution for x^2-4096x-16384=0 equation:

x^2-4096x-16384=0

a = 1; b = -4096; c = -16384;
Δ = b2-4ac
Δ = -40962-4·1·(-16384)
Δ = 16842752
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:

$\sqrt{\Delta}=\sqrt{16842752}=\sqrt{65536*257}=\sqrt{65536}*\sqrt{257}=256\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4096)-256\sqrt{257}}{2*1}=\frac{4096-256\sqrt{257}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4096)+256\sqrt{257}}{2*1}=\frac{4096+256\sqrt{257}}{2}
$