18x(-6-1/3)=x

Solution for 18x(-6-1/3)=x equation:

18x(-6-1/3)=x

We move all terms to the left:

18x(-6-1/3)-(x)=0

We add all the numbers together, and all the variables

18x(-1/3-6)-x=0

We add all the numbers together, and all the variables

-1x+18x(-1/3-6)=0

We multiply parentheses

-18x^2-1x-108x=0

We add all the numbers together, and all the variables

-18x^2-109x=0

a = -18; b = -109; c = 0;
Δ = b2-4ac
Δ = -1092-4·(-18)·0
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-109}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+109}{2*-18}=\frac{218}{-36}
=-6+1/18
$