x+20/100x=26

Solution for x+20/100x=26 equation:

x+20/100x=26

We move all terms to the left:

x+20/100x-(26)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-26*100x+20=0

Wy multiply elements

100x^2-2600x+20=0

a = 100; b = -2600; c = +20;
Δ = b2-4ac
Δ = -26002-4·100·20
Δ = 6752000
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:

$\sqrt{\Delta}=\sqrt{6752000}=\sqrt{6400*1055}=\sqrt{6400}*\sqrt{1055}=80\sqrt{1055}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2600)-80\sqrt{1055}}{2*100}=\frac{2600-80\sqrt{1055}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2600)+80\sqrt{1055}}{2*100}=\frac{2600+80\sqrt{1055}}{200}
$