X/5^x+1+5^1-x=26

Solution for X/5^x+1+5^1-x=26 equation:

X/5^X+1+5^1-X=26

We move all terms to the left:

X/5^X+1+5^1-X-(26)=0


Domain of the equation: 5^X!=0

X!=0/1

X!=0

X∈R


determiningTheFunctionDomain
X/5^X-X+1-26+5^1=0

We add all the numbers together, and all the variables

-1X+X/5^X-20=0

We multiply all the terms by the denominator


-1X*5^X+X-20*5^X=0

We add all the numbers together, and all the variables

X-1X*5^X-20*5^X=0

Wy multiply elements

-5X^2+X-100X=0

We add all the numbers together, and all the variables

-5X^2-99X=0

a = -5; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·(-5)·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*-5}=\frac{0}{-10}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*-5}=\frac{198}{-10}
=-19+4/5
$