2/3x-18=6x

Solution for 2/3x-18=6x equation:

2/3x-18=6x

We move all terms to the left:

2/3x-18-(6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+2/3x-18=0

We multiply all the terms by the denominator


-6x*3x-18*3x+2=0

Wy multiply elements

-18x^2-54x+2=0

a = -18; b = -54; c = +2;
Δ = b2-4ac
Δ = -542-4·(-18)·2
Δ = 3060
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{85}}{2*-18}=\frac{54-6\sqrt{85}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{85}}{2*-18}=\frac{54+6\sqrt{85}}{-36}
$