4/3x=8x=6

Solution for 4/3x=8x=6 equation:

4/3x=8x=6

We move all terms to the left:

4/3x-(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+4/3x=0

We multiply all the terms by the denominator


-8x*3x+4=0

Wy multiply elements

-24x^2+4=0

a = -24; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-24)·4
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*-24}=\frac{0-8\sqrt{6}}{-48}
=-\frac{8\sqrt{6}}{-48}
=-\frac{\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*-24}=\frac{0+8\sqrt{6}}{-48}
=\frac{8\sqrt{6}}{-48}
=\frac{\sqrt{6}}{-6}
$