81x^2-125=0

Solution for 81x^2-125=0 equation:

81x^2-125=0

a = 81; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·81·(-125)
Δ = 40500
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:

$\sqrt{\Delta}=\sqrt{40500}=\sqrt{8100*5}=\sqrt{8100}*\sqrt{5}=90\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90\sqrt{5}}{2*81}=\frac{0-90\sqrt{5}}{162}
=-\frac{90\sqrt{5}}{162}
=-\frac{5\sqrt{5}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90\sqrt{5}}{2*81}=\frac{0+90\sqrt{5}}{162}
=\frac{90\sqrt{5}}{162}
=\frac{5\sqrt{5}}{9}
$