2/3(x)-12x=18

Solution for 2/3(x)-12x=18 equation:

2/3(x)-12x=18

We move all terms to the left:

2/3(x)-12x-(18)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-12x+2/3x-18=0

We multiply all the terms by the denominator


-12x*3x-18*3x+2=0

Wy multiply elements

-36x^2-54x+2=0

a = -36; b = -54; c = +2;
Δ = b2-4ac
Δ = -542-4·(-36)·2
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{89}}{2*-36}=\frac{54-6\sqrt{89}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{89}}{2*-36}=\frac{54+6\sqrt{89}}{-72}
$