(-16x^2)+64x+5=0

Solution for (-16x^2)+64x+5=0 equation:

(-16x^2)+64x+5=0

We get rid of parentheses

-16x^2+64x+5=0

a = -16; b = 64; c = +5;
Δ = b2-4ac
Δ = 642-4·(-16)·5
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{69}}{2*-16}=\frac{-64-8\sqrt{69}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{69}}{2*-16}=\frac{-64+8\sqrt{69}}{-32}
$