16x^2-128x-4096=0

Solution for 16x^2-128x-4096=0 equation:

16x^2-128x-4096=0

a = 16; b = -128; c = -4096;
Δ = b2-4ac
Δ = -1282-4·16·(-4096)
Δ = 278528
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:

$\sqrt{\Delta}=\sqrt{278528}=\sqrt{16384*17}=\sqrt{16384}*\sqrt{17}=128\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128\sqrt{17}}{2*16}=\frac{128-128\sqrt{17}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128\sqrt{17}}{2*16}=\frac{128+128\sqrt{17}}{32}
$