9k^2-8k-3=0

Solution for 9k^2-8k-3=0 equation:

9k^2-8k-3=0

a = 9; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·9·(-3)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{43}}{2*9}=\frac{8-2\sqrt{43}}{18}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{43}}{2*9}=\frac{8+2\sqrt{43}}{18}
$