x+8/4x+1=x-3/x

Solution for x+8/4x+1=x-3/x equation:

x+8/4x+1=x-3/x

We move all terms to the left:

x+8/4x+1-(x-3/x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+8/4x-(+x-3/x)+1=0

We get rid of parentheses

x+8/4x-x+3/x+1=0

We calculate fractions


x-x+8x/4x^2+12x/4x^2+1=0

We add all the numbers together, and all the variables

8x/4x^2+12x/4x^2+1=0

We multiply all the terms by the denominator


8x+12x+1*4x^2=0

We add all the numbers together, and all the variables

20x+1*4x^2=0

Wy multiply elements

4x^2+20x=0

a = 4; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·4·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*4}=\frac{0}{8}
=0
$