x+(12/100*x)=27

Solution for x+(12/100*x)=27 equation:

x+(12/100x)=27

We move all terms to the left:

x+(12/100x)-(27)=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)-27=0

We get rid of parentheses

x+12/100x-27=0

We multiply all the terms by the denominator


x*100x-27*100x+12=0

Wy multiply elements

100x^2-2700x+12=0

a = 100; b = -2700; c = +12;
Δ = b2-4ac
Δ = -27002-4·100·12
Δ = 7285200
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:

$\sqrt{\Delta}=\sqrt{7285200}=\sqrt{400*18213}=\sqrt{400}*\sqrt{18213}=20\sqrt{18213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2700)-20\sqrt{18213}}{2*100}=\frac{2700-20\sqrt{18213}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2700)+20\sqrt{18213}}{2*100}=\frac{2700+20\sqrt{18213}}{200}
$