2x+8+2/3x=64

Solution for 2x+8+2/3x=64 equation:

2x+8+2/3x=64

We move all terms to the left:

2x+8+2/3x-(64)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+2/3x-56=0

We multiply all the terms by the denominator


2x*3x-56*3x+2=0

Wy multiply elements

6x^2-168x+2=0

a = 6; b = -168; c = +2;
Δ = b2-4ac
Δ = -1682-4·6·2
Δ = 28176
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:

$\sqrt{\Delta}=\sqrt{28176}=\sqrt{16*1761}=\sqrt{16}*\sqrt{1761}=4\sqrt{1761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-4\sqrt{1761}}{2*6}=\frac{168-4\sqrt{1761}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+4\sqrt{1761}}{2*6}=\frac{168+4\sqrt{1761}}{12}
$