16k^2-108k+64=0

Solution for 16k^2-108k+64=0 equation:

16k^2-108k+64=0

a = 16; b = -108; c = +64;
Δ = b2-4ac
Δ = -1082-4·16·64
Δ = 7568
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7568}=\sqrt{16*473}=\sqrt{16}*\sqrt{473}=4\sqrt{473}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{473}}{2*16}=\frac{108-4\sqrt{473}}{32}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{473}}{2*16}=\frac{108+4\sqrt{473}}{32}
$