8/3x+4=x

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

8/3x+4=x

We move all terms to the left:

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

We multiply all the terms by the denominator


-1x*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}
$