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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x+x/6x-27=0

We multiply all the terms by the denominator


3x*6x+x-27*6x=0

We add all the numbers together, and all the variables

x+3x*6x-27*6x=0

Wy multiply elements

18x^2+x-162x=0

We add all the numbers together, and all the variables

18x^2-161x=0

a = 18; b = -161; c = 0;
Δ = b2-4ac
Δ = -1612-4·18·0
Δ = 25921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25921}=161$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-161)-161}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-161)+161}{2*18}=\frac{322}{36}
=8+17/18
$