x-(20/100*x)=8

Solution for x-(20/100*x)=8 equation:

x-(20/100x)=8

We move all terms to the left:

x-(20/100x)-(8)=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-(+20/100x)-8=0

We get rid of parentheses

x-20/100x-8=0

We multiply all the terms by the denominator


x*100x-8*100x-20=0

Wy multiply elements

100x^2-800x-20=0

a = 100; b = -800; c = -20;
Δ = b2-4ac
Δ = -8002-4·100·(-20)
Δ = 648000
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:

$\sqrt{\Delta}=\sqrt{648000}=\sqrt{129600*5}=\sqrt{129600}*\sqrt{5}=360\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-360\sqrt{5}}{2*100}=\frac{800-360\sqrt{5}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+360\sqrt{5}}{2*100}=\frac{800+360\sqrt{5}}{200}
$