x-1/5x=100

Solution for x-1/5x=100 equation:

x-1/5x=100

We move all terms to the left:

x-1/5x-(100)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-100*5x-1=0

Wy multiply elements

5x^2-500x-1=0

a = 5; b = -500; c = -1;
Δ = b2-4ac
Δ = -5002-4·5·(-1)
Δ = 250020
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:

$\sqrt{\Delta}=\sqrt{250020}=\sqrt{36*6945}=\sqrt{36}*\sqrt{6945}=6\sqrt{6945}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-6\sqrt{6945}}{2*5}=\frac{500-6\sqrt{6945}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+6\sqrt{6945}}{2*5}=\frac{500+6\sqrt{6945}}{10}
$