2/3x-4=8x

Solution for 2/3x-4=8x equation:

2/3x-4=8x

We move all terms to the left:

2/3x-4-(8x)=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-4=0

We multiply all the terms by the denominator


-8x*3x-4*3x+2=0

Wy multiply elements

-24x^2-12x+2=0

a = -24; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-24)·2
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{21}}{2*-24}=\frac{12-4\sqrt{21}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{21}}{2*-24}=\frac{12+4\sqrt{21}}{-48}
$