x2-(x-4)2=128

Solution for x2-(x-4)2=128 equation:

x2-(x-4)2=128

We move all terms to the left:

x2-(x-4)2-(128)=0

We add all the numbers together, and all the variables

x^2-(x-4)2-128=0

We multiply parentheses

x^2-2x+8-128=0

We add all the numbers together, and all the variables

x^2-2x-120=0

a = 1; b = -2; c = -120;
Δ = b2-4ac
Δ = -22-4·1·(-120)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*1}=\frac{24}{2}
=12
$