X2-4x-128=0

Solution for X2-4x-128=0 equation:

X2-4X-128=0

We add all the numbers together, and all the variables

X^2-4X-128=0

a = 1; b = -4; c = -128;
Δ = b2-4ac
Δ = -42-4·1·(-128)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{33}}{2*1}=\frac{4-4\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{33}}{2*1}=\frac{4+4\sqrt{33}}{2}
$