X/6x-27+3x=4+9-x

Solution for X/6x-27+3x=4+9-x equation:

X/6X-27+3X=4+9-X

We move all terms to the left:

X/6X-27+3X-(4+9-X)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We add all the numbers together, and all the variables

X/6X+3X-(-1X+13)-27=0

We add all the numbers together, and all the variables

3X+X/6X-(-1X+13)-27=0

We get rid of parentheses

3X+X/6X+1X-13-27=0

We multiply all the terms by the denominator


3X*6X+X+1X*6X-13*6X-27*6X=0

We add all the numbers together, and all the variables

X+3X*6X+1X*6X-13*6X-27*6X=0

Wy multiply elements

18X^2+6X^2+X-78X-162X=0

We add all the numbers together, and all the variables

24X^2-239X=0

a = 24; b = -239; c = 0;
Δ = b2-4ac
Δ = -2392-4·24·0
Δ = 57121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57121}=239$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-239)-239}{2*24}=\frac{0}{48}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-239)+239}{2*24}=\frac{478}{48}
=9+23/24
$