9k^2-12k-8=0

Solution for 9k^2-12k-8=0 equation:

9k^2-12k-8=0

a = 9; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·9·(-8)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{3}}{2*9}=\frac{12-12\sqrt{3}}{18}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{3}}{2*9}=\frac{12+12\sqrt{3}}{18}
$