x-(75/100*x)=600

Solution for x-(75/100*x)=600 equation:

x-(75/100x)=600

We move all terms to the left:

x-(75/100x)-(600)=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-(+75/100x)-600=0

We get rid of parentheses

x-75/100x-600=0

We multiply all the terms by the denominator


x*100x-600*100x-75=0

Wy multiply elements

100x^2-60000x-75=0

a = 100; b = -60000; c = -75;
Δ = b2-4ac
Δ = -600002-4·100·(-75)
Δ = 3600030000
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:

$\sqrt{\Delta}=\sqrt{3600030000}=\sqrt{490000*7347}=\sqrt{490000}*\sqrt{7347}=700\sqrt{7347}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60000)-700\sqrt{7347}}{2*100}=\frac{60000-700\sqrt{7347}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60000)+700\sqrt{7347}}{2*100}=\frac{60000+700\sqrt{7347}}{200}
$