2/3x-8x=12

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

2/3x-8x=12

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -24; b = -36; c = +2;
Δ = b2-4ac
Δ = -362-4·(-24)·2
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{93}}{2*-24}=\frac{36-4\sqrt{93}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{93}}{2*-24}=\frac{36+4\sqrt{93}}{-48}
$