(51/5)^5=25^x

Solution for (51/5)^5=25^x equation:

(51/5)^5=25^x

We move all terms to the left:

(51/5)^5-(25^x)=0

We add all the numbers together, and all the variables

-25^x+(+51/5)^5=0

We multiply all the terms by the denominator


-25^x*5)^5+(+51=0

Wy multiply elements

-125x^2+51=0

a = -125; b = 0; c = +51;
Δ = b2-4ac
Δ = 02-4·(-125)·51
Δ = 25500
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:

$\sqrt{\Delta}=\sqrt{25500}=\sqrt{100*255}=\sqrt{100}*\sqrt{255}=10\sqrt{255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{255}}{2*-125}=\frac{0-10\sqrt{255}}{-250}
=-\frac{10\sqrt{255}}{-250}
=-\frac{\sqrt{255}}{-25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{255}}{2*-125}=\frac{0+10\sqrt{255}}{-250}
=\frac{10\sqrt{255}}{-250}
=\frac{\sqrt{255}}{-25}
$