x+(12/100*x)=1800

Solution for x+(12/100*x)=1800 equation:

x+(12/100x)=1800

We move all terms to the left:

x+(12/100x)-(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+(+12/100x)-1800=0

We get rid of parentheses

x+12/100x-1800=0

We multiply all the terms by the denominator


x*100x-1800*100x+12=0

Wy multiply elements

100x^2-180000x+12=0

a = 100; b = -180000; c = +12;
Δ = b2-4ac
Δ = -1800002-4·100·12
Δ = 32399995200
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:

$\sqrt{\Delta}=\sqrt{32399995200}=\sqrt{1600*20249997}=\sqrt{1600}*\sqrt{20249997}=40\sqrt{20249997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180000)-40\sqrt{20249997}}{2*100}=\frac{180000-40\sqrt{20249997}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180000)+40\sqrt{20249997}}{2*100}=\frac{180000+40\sqrt{20249997}}{200}
$