16k^2-36k-9=0

Solution for 16k^2-36k-9=0 equation:

16k^2-36k-9=0

a = 16; b = -36; c = -9;
Δ = b2-4ac
Δ = -362-4·16·(-9)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{13}}{2*16}=\frac{36-12\sqrt{13}}{32}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{13}}{2*16}=\frac{36+12\sqrt{13}}{32}
$