81k^2-32=0

Solution for 81k^2-32=0 equation:

81k^2-32=0

a = 81; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·81·(-32)
Δ = 10368
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:

$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{2}}{2*81}=\frac{0-72\sqrt{2}}{162}
=-\frac{72\sqrt{2}}{162}
=-\frac{4\sqrt{2}}{9}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{2}}{2*81}=\frac{0+72\sqrt{2}}{162}
=\frac{72\sqrt{2}}{162}
=\frac{4\sqrt{2}}{9}
$