x-2/4x-3=x+8/x

Solution for x-2/4x-3=x+8/x equation:

x-2/4x-3=x+8/x

We move all terms to the left:

x-2/4x-3-(x+8/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-2/4x-(+x+8/x)-3=0

We get rid of parentheses

x-2/4x-x-8/x-3=0

We calculate fractions


x-x+(-2x)/4x^2+(-32x)/4x^2-3=0

We add all the numbers together, and all the variables

(-2x)/4x^2+(-32x)/4x^2-3=0

We multiply all the terms by the denominator


(-2x)+(-32x)-3*4x^2=0

Wy multiply elements

-12x^2+(-2x)+(-32x)=0

We get rid of parentheses

-12x^2-2x-32x=0

We add all the numbers together, and all the variables

-12x^2-34x=0

a = -12; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·(-12)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*-12}=\frac{68}{-24}
=-2+5/6
$