16k^2-8k-27=0

Solution for 16k^2-8k-27=0 equation:

16k^2-8k-27=0

a = 16; b = -8; c = -27;
Δ = b2-4ac
Δ = -82-4·16·(-27)
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{7}}{2*16}=\frac{8-16\sqrt{7}}{32}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{7}}{2*16}=\frac{8+16\sqrt{7}}{32}
$