3/x+6=6/8x-12

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Solution for 3/x+6=6/8x-12 equation: 



3/x+6=6/8x-12

We move all terms to the left:

3/x+6-(6/8x-12)=0



Domain of the equation: x!=0

x∈R





Domain of the equation: 8x-12)!=0

x∈R



We get rid of parentheses

3/x-6/8x+12+6=0

We calculate fractions


24x/8x^2+(-6x)/8x^2+12+6=0

We add all the numbers together, and all the variables

24x/8x^2+(-6x)/8x^2+18=0

We multiply all the terms by the denominator


24x+(-6x)+18*8x^2=0

Wy multiply elements

144x^2+24x+(-6x)=0

We get rid of parentheses

144x^2+24x-6x=0

We add all the numbers together, and all the variables

144x^2+18x=0

a = 144; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·144·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*144}=\frac{-36}{288}
=-1/8
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*144}=\frac{0}{288}
=0
$

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