x=100x/80x

Solution for x=100x/80x equation:

x=100x/80x

We move all terms to the left:

x-(100x/80x)=0


Domain of the equation: 80x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+100x/80x)=0

We get rid of parentheses

x-100x/80x=0

We multiply all the terms by the denominator


x*80x-100x=0

We add all the numbers together, and all the variables

-100x+x*80x=0

Wy multiply elements

80x^2-100x=0

a = 80; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·80·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*80}=\frac{0}{160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*80}=\frac{200}{160}
=1+1/4
$