250=x+5/100*x

Solution for 250=x+5/100*x equation:

250=x+5/100x

We move all terms to the left:

250-(x+5/100x)=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+5/100x)+250=0

We get rid of parentheses

-x-5/100x+250=0

We multiply all the terms by the denominator


-x*100x+250*100x-5=0

Wy multiply elements

-100x^2+25000x-5=0

a = -100; b = 25000; c = -5;
Δ = b2-4ac
Δ = 250002-4·(-100)·(-5)
Δ = 624998000
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:

$\sqrt{\Delta}=\sqrt{624998000}=\sqrt{400*1562495}=\sqrt{400}*\sqrt{1562495}=20\sqrt{1562495}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25000)-20\sqrt{1562495}}{2*-100}=\frac{-25000-20\sqrt{1562495}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25000)+20\sqrt{1562495}}{2*-100}=\frac{-25000+20\sqrt{1562495}}{-200}
$