8/2x-6=3/x+2

Solution for 8/2x-6=3/x+2 equation:

8/2x-6=3/x+2

We move all terms to the left:

8/2x-6-(3/x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

8/2x-3/x-2-6=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


8x+(-6x)-8*2x^2=0

Wy multiply elements

-16x^2+8x+(-6x)=0

We get rid of parentheses

-16x^2+8x-6x=0

We add all the numbers together, and all the variables

-16x^2+2x=0

a = -16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-16)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-16}=\frac{-4}{-32}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-16}=\frac{0}{-32}
=0
$