x+(5/100*x)=1800

Solution for x+(5/100*x)=1800 equation:

x+(5/100x)=1800

We move all terms to the left:

x+(5/100x)-(1800)=0


Domain of the equation: 100x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+5/100x)-1800=0

We get rid of parentheses

x+5/100x-1800=0

We multiply all the terms by the denominator


x*100x-1800*100x+5=0

Wy multiply elements

100x^2-180000x+5=0

a = 100; b = -180000; c = +5;
Δ = b2-4ac
Δ = -1800002-4·100·5
Δ = 32399998000
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:

$\sqrt{\Delta}=\sqrt{32399998000}=\sqrt{400*80999995}=\sqrt{400}*\sqrt{80999995}=20\sqrt{80999995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180000)-20\sqrt{80999995}}{2*100}=\frac{180000-20\sqrt{80999995}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180000)+20\sqrt{80999995}}{2*100}=\frac{180000+20\sqrt{80999995}}{200}
$