8/x+1=12/2x-6

Solution for 8/x+1=12/2x-6 equation:

8/x+1=12/2x-6

We move all terms to the left:

8/x+1-(12/2x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

8/x-12/2x+6+1=0

We calculate fractions


16x/2x^2+(-12x)/2x^2+6+1=0

We add all the numbers together, and all the variables

16x/2x^2+(-12x)/2x^2+7=0

We multiply all the terms by the denominator


16x+(-12x)+7*2x^2=0

Wy multiply elements

14x^2+16x+(-12x)=0

We get rid of parentheses

14x^2+16x-12x=0

We add all the numbers together, and all the variables

14x^2+4x=0

a = 14; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·14·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*14}=\frac{-8}{28}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*14}=\frac{0}{28}
=0
$