0=-4x^2+64x+128

Solution for 0=-4x^2+64x+128 equation:

0=-4x^2+64x+128

We move all terms to the left:

0-(-4x^2+64x+128)=0

We add all the numbers together, and all the variables

-(-4x^2+64x+128)=0

We get rid of parentheses

4x^2-64x-128=0

a = 4; b = -64; c = -128;
Δ = b2-4ac
Δ = -642-4·4·(-128)
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-32\sqrt{6}}{2*4}=\frac{64-32\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32\sqrt{6}}{2*4}=\frac{64+32\sqrt{6}}{8}
$