8-2/3x=x

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

8-2/3x=x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-2/3x+8=0

We multiply all the terms by the denominator


-1x*3x+8*3x-2=0

Wy multiply elements

-3x^2+24x-2=0

a = -3; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·(-3)·(-2)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{138}}{2*-3}=\frac{-24-2\sqrt{138}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{138}}{2*-3}=\frac{-24+2\sqrt{138}}{-6}
$