5^2x-1=1/125

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

5^2x-1=1/125

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5^2x*125-126=0

Wy multiply elements

625x^2-126=0

a = 625; b = 0; c = -126;
Δ = b2-4ac
Δ = 02-4·625·(-126)
Δ = 315000
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:

$\sqrt{\Delta}=\sqrt{315000}=\sqrt{22500*14}=\sqrt{22500}*\sqrt{14}=150\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150\sqrt{14}}{2*625}=\frac{0-150\sqrt{14}}{1250}
=-\frac{150\sqrt{14}}{1250}
=-\frac{3\sqrt{14}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150\sqrt{14}}{2*625}=\frac{0+150\sqrt{14}}{1250}
=\frac{150\sqrt{14}}{1250}
=\frac{3\sqrt{14}}{25}
$