x-(25/100*x)=100

Solution for x-(25/100*x)=100 equation:

x-(25/100x)=100

We move all terms to the left:

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

We get rid of parentheses

x-25/100x-100=0

We multiply all the terms by the denominator


x*100x-100*100x-25=0

Wy multiply elements

100x^2-10000x-25=0

a = 100; b = -10000; c = -25;
Δ = b2-4ac
Δ = -100002-4·100·(-25)
Δ = 100010000
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:

$\sqrt{\Delta}=\sqrt{100010000}=\sqrt{10000*10001}=\sqrt{10000}*\sqrt{10001}=100\sqrt{10001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10000)-100\sqrt{10001}}{2*100}=\frac{10000-100\sqrt{10001}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10000)+100\sqrt{10001}}{2*100}=\frac{10000+100\sqrt{10001}}{200}
$