x-8/3x=4

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

x-8/3x=4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-12x-8=0

a = 3; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·3·(-8)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*3}=\frac{12-4\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*3}=\frac{12+4\sqrt{15}}{6}
$