8/x+5=12/4x

Solution for 8/x+5=12/4x equation:

8/x+5=12/4x

We move all terms to the left:

8/x+5-(12/4x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/x-(+12/4x)+5=0

We get rid of parentheses

8/x-12/4x+5=0

We calculate fractions


32x/4x^2+(-12x)/4x^2+5=0

We multiply all the terms by the denominator


32x+(-12x)+5*4x^2=0

Wy multiply elements

20x^2+32x+(-12x)=0

We get rid of parentheses

20x^2+32x-12x=0

We add all the numbers together, and all the variables

20x^2+20x=0

a = 20; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·20·0
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*20}=\frac{-40}{40}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*20}=\frac{0}{40}
=0
$