x^2-48x-128=0

Solution for x^2-48x-128=0 equation:

x^2-48x-128=0

a = 1; b = -48; c = -128;
Δ = b2-4ac
Δ = -482-4·1·(-128)
Δ = 2816
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:

$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-16\sqrt{11}}{2*1}=\frac{48-16\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+16\sqrt{11}}{2*1}=\frac{48+16\sqrt{11}}{2}
$