5^2x-4=1/125

Solution for 5^2x-4=1/125 equation:

5^2x-4=1/125

We move all terms to the left:

5^2x-4-(1/125)=0

We add all the numbers together, and all the variables

5^2x-4-(+1/125)=0

We get rid of parentheses

5^2x-4-1/125=0

We multiply all the terms by the denominator


5^2x*125-1-4*125=0

We add all the numbers together, and all the variables

5^2x*125-501=0

Wy multiply elements

625x^2-501=0

a = 625; b = 0; c = -501;
Δ = b2-4ac
Δ = 02-4·625·(-501)
Δ = 1252500
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:

$\sqrt{\Delta}=\sqrt{1252500}=\sqrt{2500*501}=\sqrt{2500}*\sqrt{501}=50\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{501}}{2*625}=\frac{0-50\sqrt{501}}{1250}
=-\frac{50\sqrt{501}}{1250}
=-\frac{\sqrt{501}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{501}}{2*625}=\frac{0+50\sqrt{501}}{1250}
=\frac{50\sqrt{501}}{1250}
=\frac{\sqrt{501}}{25}
$