8/x-2=5/6x

Solution for 8/x-2=5/6x equation:

8/x-2=5/6x

We move all terms to the left:

8/x-2-(5/6x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/x-(+5/6x)-2=0

We get rid of parentheses

8/x-5/6x-2=0

We calculate fractions


48x/6x^2+(-5x)/6x^2-2=0

We multiply all the terms by the denominator


48x+(-5x)-2*6x^2=0

Wy multiply elements

-12x^2+48x+(-5x)=0

We get rid of parentheses

-12x^2+48x-5x=0

We add all the numbers together, and all the variables

-12x^2+43x=0

a = -12; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-12)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-12}=\frac{-86}{-24}
=3+7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-12}=\frac{0}{-24}
=0
$