0=-8x^2+16x-5

Solution for 0=-8x^2+16x-5 equation:

0=-8x^2+16x-5

We move all terms to the left:

0-(-8x^2+16x-5)=0

We add all the numbers together, and all the variables

-(-8x^2+16x-5)=0

We get rid of parentheses

8x^2-16x+5=0

a = 8; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·8·5
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{6}}{2*8}=\frac{16-4\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{6}}{2*8}=\frac{16+4\sqrt{6}}{16}
$