8x-4/3x=2

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

8x-4/3x=2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

24x^2-6x-4=0

a = 24; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·24·(-4)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{105}}{2*24}=\frac{6-2\sqrt{105}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{105}}{2*24}=\frac{6+2\sqrt{105}}{48}
$