180=x+25/100*x

Solution for 180=x+25/100*x equation:

180=x+25/100x

We move all terms to the left:

180-(x+25/100x)=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+25/100x)+180=0

We get rid of parentheses

-x-25/100x+180=0

We multiply all the terms by the denominator


-x*100x+180*100x-25=0

Wy multiply elements

-100x^2+18000x-25=0

a = -100; b = 18000; c = -25;
Δ = b2-4ac
Δ = 180002-4·(-100)·(-25)
Δ = 323990000
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:

$\sqrt{\Delta}=\sqrt{323990000}=\sqrt{10000*32399}=\sqrt{10000}*\sqrt{32399}=100\sqrt{32399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18000)-100\sqrt{32399}}{2*-100}=\frac{-18000-100\sqrt{32399}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18000)+100\sqrt{32399}}{2*-100}=\frac{-18000+100\sqrt{32399}}{-200}
$