128x-64=16x^2

Solution for 128x-64=16x^2 equation:

128x-64=16x^2

We move all terms to the left:

128x-64-(16x^2)=0

determiningTheFunctionDomain
-16x^2+128x-64=0

a = -16; b = 128; c = -64;
Δ = b2-4ac
Δ = 1282-4·(-16)·(-64)
Δ = 12288
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:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-64\sqrt{3}}{2*-16}=\frac{-128-64\sqrt{3}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+64\sqrt{3}}{2*-16}=\frac{-128+64\sqrt{3}}{-32}
$