5^x=25/5^x

Solution for 5^x=25/5^x equation:

5^x=25/5^x

We move all terms to the left:

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


Domain of the equation: 5^x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

5^x-25/5^x=0

We multiply all the terms by the denominator


5^x*5^x-25=0

Wy multiply elements

25x^2-25=0

a = 25; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·25·(-25)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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