-16x^2+128+5=0

Solution for -16x^2+128+5=0 equation:

-16x^2+128+5=0

We add all the numbers together, and all the variables

-16x^2+133=0

a = -16; b = 0; c = +133;
Δ = b2-4ac
Δ = 02-4·(-16)·133
Δ = 8512
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:

$\sqrt{\Delta}=\sqrt{8512}=\sqrt{64*133}=\sqrt{64}*\sqrt{133}=8\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{133}}{2*-16}=\frac{0-8\sqrt{133}}{-32}
=-\frac{8\sqrt{133}}{-32}
=-\frac{\sqrt{133}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{133}}{2*-16}=\frac{0+8\sqrt{133}}{-32}
=\frac{8\sqrt{133}}{-32}
=\frac{\sqrt{133}}{-4}
$