81x2-192=0

Solution for 81x2-192=0 equation:

81x^2-192=0

a = 81; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·81·(-192)
Δ = 62208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{62208}=\sqrt{20736*3}=\sqrt{20736}*\sqrt{3}=144\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{3}}{2*81}=\frac{0-144\sqrt{3}}{162}
=-\frac{144\sqrt{3}}{162}
=-\frac{8\sqrt{3}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{3}}{2*81}=\frac{0+144\sqrt{3}}{162}
=\frac{144\sqrt{3}}{162}
=\frac{8\sqrt{3}}{9}
$