5x/8x=x/100

Solution for 5x/8x=x/100 equation:

5x/8x=x/100

We move all terms to the left:

5x/8x-(x/100)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

5x/8x-(+x/100)=0

We get rid of parentheses

5x/8x-x/100=0

We calculate fractions


(-8x^2)/800x+500x/800x=0

We multiply all the terms by the denominator


(-8x^2)+500x=0

We get rid of parentheses

-8x^2+500x=0

a = -8; b = 500; c = 0;
Δ = b2-4ac
Δ = 5002-4·(-8)·0
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-500}{2*-8}=\frac{-1000}{-16}
=62+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+500}{2*-8}=\frac{0}{-16}
=0
$