130=x+18/100x

Solution for 130=x+18/100x equation:

130=x+18/100x

We move all terms to the left:

130-(x+18/100x)=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+18/100x)+130=0

We get rid of parentheses

-x-18/100x+130=0

We multiply all the terms by the denominator


-x*100x+130*100x-18=0

Wy multiply elements

-100x^2+13000x-18=0

a = -100; b = 13000; c = -18;
Δ = b2-4ac
Δ = 130002-4·(-100)·(-18)
Δ = 168992800
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:

$\sqrt{\Delta}=\sqrt{168992800}=\sqrt{400*422482}=\sqrt{400}*\sqrt{422482}=20\sqrt{422482}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13000)-20\sqrt{422482}}{2*-100}=\frac{-13000-20\sqrt{422482}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13000)+20\sqrt{422482}}{2*-100}=\frac{-13000+20\sqrt{422482}}{-200}
$