0=-16x^2+64x-52

Solution for 0=-16x^2+64x-52 equation:

0=-16x^2+64x-52

We move all terms to the left:

0-(-16x^2+64x-52)=0

We add all the numbers together, and all the variables

-(-16x^2+64x-52)=0

We get rid of parentheses

16x^2-64x+52=0

a = 16; b = -64; c = +52;
Δ = b2-4ac
Δ = -642-4·16·52
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{3}}{2*16}=\frac{64-16\sqrt{3}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{3}}{2*16}=\frac{64+16\sqrt{3}}{32}
$