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X/3x-8=-2/x

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Solution for X/3x-8=-2/x equation:



X/3X-8=-2/X
We move all terms to the left:
X/3X-8-(-2/X)=0
Domain of the equation: 3X!=0
X!=0/3
X!=0
X∈R
Domain of the equation: X)!=0
X!=0/1
X!=0
X∈R
We get rid of parentheses
X/3X+2/X-8=0
We calculate fractions
X^2/3X^2+6X/3X^2-8=0
We multiply all the terms by the denominator
X^2+6X-8*3X^2=0
Wy multiply elements
X^2-24X^2+6X=0
We add all the numbers together, and all the variables
-23X^2+6X=0
a = -23; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-23)·0
Δ = 36
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{36}=6
X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-23}=\frac{-12}{-46} =6/23
X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-23}=\frac{0}{-46} =0

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