25^2x-3=1/125

Solution for 25^2x-3=1/125 equation:

25^2x-3=1/125

We move all terms to the left:

25^2x-3-(1/125)=0

We add all the numbers together, and all the variables

25^2x-3-(+1/125)=0

We get rid of parentheses

25^2x-3-1/125=0

We multiply all the terms by the denominator


25^2x*125-1-3*125=0

We add all the numbers together, and all the variables

25^2x*125-376=0

Wy multiply elements

3125x^2-376=0

a = 3125; b = 0; c = -376;
Δ = b2-4ac
Δ = 02-4·3125·(-376)
Δ = 4700000
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:

$\sqrt{\Delta}=\sqrt{4700000}=\sqrt{10000*470}=\sqrt{10000}*\sqrt{470}=100\sqrt{470}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{470}}{2*3125}=\frac{0-100\sqrt{470}}{6250}
=-\frac{100\sqrt{470}}{6250}
=-\frac{2\sqrt{470}}{125}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{470}}{2*3125}=\frac{0+100\sqrt{470}}{6250}
=\frac{100\sqrt{470}}{6250}
=\frac{2\sqrt{470}}{125}
$