2/3x-12x=8

Solution for 2/3x-12x=8 equation:

2/3x-12x=8

We move all terms to the left:

2/3x-12x-(8)=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-8=0

We multiply all the terms by the denominator


-12x*3x-8*3x+2=0

Wy multiply elements

-36x^2-24x+2=0

a = -36; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·(-36)·2
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{6}}{2*-36}=\frac{24-12\sqrt{6}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{6}}{2*-36}=\frac{24+12\sqrt{6}}{-72}
$