128x-16x^2=208

Solution for 128x-16x^2=208 equation:

128x-16x^2=208

We move all terms to the left:

128x-16x^2-(208)=0

a = -16; b = 128; c = -208;
Δ = b2-4ac
Δ = 1282-4·(-16)·(-208)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-32\sqrt{3}}{2*-16}=\frac{-128-32\sqrt{3}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+32\sqrt{3}}{2*-16}=\frac{-128+32\sqrt{3}}{-32}
$