x-18=15/100x

Solution for x-18=15/100x equation:

x-18=15/100x

We move all terms to the left:

x-18-(15/100x)=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-(+15/100x)-18=0

We get rid of parentheses

x-15/100x-18=0

We multiply all the terms by the denominator


x*100x-18*100x-15=0

Wy multiply elements

100x^2-1800x-15=0

a = 100; b = -1800; c = -15;
Δ = b2-4ac
Δ = -18002-4·100·(-15)
Δ = 3246000
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:

$\sqrt{\Delta}=\sqrt{3246000}=\sqrt{400*8115}=\sqrt{400}*\sqrt{8115}=20\sqrt{8115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1800)-20\sqrt{8115}}{2*100}=\frac{1800-20\sqrt{8115}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1800)+20\sqrt{8115}}{2*100}=\frac{1800+20\sqrt{8115}}{200}
$