x/6x=18+4x

Solution for x/6x=18+4x equation:

x/6x=18+4x

We move all terms to the left:

x/6x-(18+4x)=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-(4x+18)=0

We get rid of parentheses

x/6x-4x-18=0

We multiply all the terms by the denominator


x-4x*6x-18*6x=0

Wy multiply elements

-24x^2+x-108x=0

We add all the numbers together, and all the variables

-24x^2-107x=0

a = -24; b = -107; c = 0;
Δ = b2-4ac
Δ = -1072-4·(-24)·0
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-107)-107}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-107)+107}{2*-24}=\frac{214}{-48}
=-4+11/24
$