X/3-4/x+2=6x/3x+6

Solution for X/3-4/x+2=6x/3x+6 equation:

X/3-4/X+2=6X/3X+6

We move all terms to the left:

X/3-4/X+2-(6X/3X+6)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: 3X+6)!=0

X∈R


We get rid of parentheses

X/3-4/X-6X/3X-6+2=0

We calculate fractions


(-6X^2)/27X^2+X^2/27X^2+(-108X)/27X^2-6+2=0

We add all the numbers together, and all the variables

(-6X^2)/27X^2+X^2/27X^2+(-108X)/27X^2-4=0

We multiply all the terms by the denominator


(-6X^2)+X^2+(-108X)-4*27X^2=0

We add all the numbers together, and all the variables

X^2+(-6X^2)+(-108X)-4*27X^2=0

Wy multiply elements

X^2+(-6X^2)-108X^2+(-108X)=0

We get rid of parentheses

X^2-6X^2-108X^2-108X=0

We add all the numbers together, and all the variables

-113X^2-108X=0

a = -113; b = -108; c = 0;
Δ = b2-4ac
Δ = -1082-4·(-113)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-108}{2*-113}=\frac{0}{-226}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+108}{2*-113}=\frac{216}{-226}
=-108/113
$