125x^2-64=0

Solution for 125x^2-64=0 equation:

125x^2-64=0

a = 125; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·125·(-64)
Δ = 32000
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:

$\sqrt{\Delta}=\sqrt{32000}=\sqrt{6400*5}=\sqrt{6400}*\sqrt{5}=80\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{5}}{2*125}=\frac{0-80\sqrt{5}}{250}
=-\frac{80\sqrt{5}}{250}
=-\frac{8\sqrt{5}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{5}}{2*125}=\frac{0+80\sqrt{5}}{250}
=\frac{80\sqrt{5}}{250}
=\frac{8\sqrt{5}}{25}
$