16z^2-64z+57=0

Solution for 16z^2-64z+57=0 equation:

16z^2-64z+57=0

a = 16; b = -64; c = +57;
Δ = b2-4ac
Δ = -642-4·16·57
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{7}}{2*16}=\frac{64-8\sqrt{7}}{32}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{7}}{2*16}=\frac{64+8\sqrt{7}}{32}
$