8/x-2=5/4x-8-2

Solution for 8/x-2=5/4x-8-2 equation:

8/x-2=5/4x-8-2

We move all terms to the left:

8/x-2-(5/4x-8-2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-8-2)!=0

We move all terms containing x to the left, all other terms to the right

4x-2)!=8

x∈R


We add all the numbers together, and all the variables

8/x-(5/4x-10)-2=0

We get rid of parentheses

8/x-5/4x+10-2=0

We calculate fractions


32x/4x^2+(-5x)/4x^2+10-2=0

We add all the numbers together, and all the variables

32x/4x^2+(-5x)/4x^2+8=0

We multiply all the terms by the denominator


32x+(-5x)+8*4x^2=0

Wy multiply elements

32x^2+32x+(-5x)=0

We get rid of parentheses

32x^2+32x-5x=0

We add all the numbers together, and all the variables

32x^2+27x=0

a = 32; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·32·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*32}=\frac{-54}{64}
=-27/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*32}=\frac{0}{64}
=0
$