100/0.8x-100/x=5

Solution for 100/0.8x-100/x=5 equation:

100/0.8x-100/x=5

We move all terms to the left:

100/0.8x-100/x-(5)=0


Domain of the equation: 0.8x!=0

x!=0/0.8

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


100x/(0.8x*x)+x/(0.8x*x)-5=0

We add all the numbers together, and all the variables

100x/(+0.8x*x)+x/(+0.8x*x)-5=0

We multiply all the terms by the denominator


100x+x-5*(+0.8x*x)=0

We add all the numbers together, and all the variables

101x-5*(+0.8x*x)=0

We multiply parentheses

-0x^2+101x=0

We add all the numbers together, and all the variables

-1x^2+101x=0

a = -1; b = 101; c = 0;
Δ = b2-4ac
Δ = 1012-4·(-1)·0
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(101)-101}{2*-1}=\frac{-202}{-2}
=+101
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(101)+101}{2*-1}=\frac{0}{-2}
=0
$