16k^2+8k-108=0

Solution for 16k^2+8k-108=0 equation:

16k^2+8k-108=0

a = 16; b = 8; c = -108;
Δ = b2-4ac
Δ = 82-4·16·(-108)
Δ = 6976
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:

$\sqrt{\Delta}=\sqrt{6976}=\sqrt{64*109}=\sqrt{64}*\sqrt{109}=8\sqrt{109}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{109}}{2*16}=\frac{-8-8\sqrt{109}}{32}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{109}}{2*16}=\frac{-8+8\sqrt{109}}{32}
$