5^2x-6=1/625

Solution for 5^2x-6=1/625 equation:

5^2x-6=1/625

We move all terms to the left:

5^2x-6-(1/625)=0

We add all the numbers together, and all the variables

5^2x-6-(+1/625)=0

We get rid of parentheses

5^2x-6-1/625=0

We multiply all the terms by the denominator


5^2x*625-1-6*625=0

We add all the numbers together, and all the variables

5^2x*625-3751=0

Wy multiply elements

3125x^2-3751=0

a = 3125; b = 0; c = -3751;
Δ = b2-4ac
Δ = 02-4·3125·(-3751)
Δ = 46887500
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:

$\sqrt{\Delta}=\sqrt{46887500}=\sqrt{302500*155}=\sqrt{302500}*\sqrt{155}=550\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-550\sqrt{155}}{2*3125}=\frac{0-550\sqrt{155}}{6250}
=-\frac{550\sqrt{155}}{6250}
=-\frac{11\sqrt{155}}{125}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+550\sqrt{155}}{2*3125}=\frac{0+550\sqrt{155}}{6250}
=\frac{550\sqrt{155}}{6250}
=\frac{11\sqrt{155}}{125}
$