x+20/100x=2500

Solution for x+20/100x=2500 equation:

x+20/100x=2500

We move all terms to the left:

x+20/100x-(2500)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-2500*100x+20=0

Wy multiply elements

100x^2-250000x+20=0

a = 100; b = -250000; c = +20;
Δ = b2-4ac
Δ = -2500002-4·100·20
Δ = 62499992000
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:

$\sqrt{\Delta}=\sqrt{62499992000}=\sqrt{1600*39062495}=\sqrt{1600}*\sqrt{39062495}=40\sqrt{39062495}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250000)-40\sqrt{39062495}}{2*100}=\frac{250000-40\sqrt{39062495}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250000)+40\sqrt{39062495}}{2*100}=\frac{250000+40\sqrt{39062495}}{200}
$