5^(2x)+1/5=26/5

Solution for 5^(2x)+1/5=26/5 equation:

5^(2x)+1/5=26/5

We move all terms to the left:

5^(2x)+1/5-(26/5)=0

We add all the numbers together, and all the variables

5^2x+1/5-(+26/5)=0

We get rid of parentheses

5^2x+1/5-26/5=0

We multiply all the terms by the denominator


5^2x*5+1-26=0

We add all the numbers together, and all the variables

5^2x*5-25=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
$