(8+1/3x)+x+(8+1/3x)+x=196

Solution for (8+1/3x)+x+(8+1/3x)+x=196 equation:

(8+1/3x)+x+(8+1/3x)+x=196

We move all terms to the left:

(8+1/3x)+x+(8+1/3x)+x-(196)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(1/3x+8)+x+(1/3x+8)+x-196=0

We add all the numbers together, and all the variables

2x+(1/3x+8)+(1/3x+8)-196=0

We get rid of parentheses

2x+1/3x+1/3x+8+8-196=0

We multiply all the terms by the denominator


2x*3x+8*3x+8*3x-196*3x+1+1=0

We add all the numbers together, and all the variables

2x*3x+8*3x+8*3x-196*3x+2=0

Wy multiply elements

6x^2+24x+24x-588x+2=0

We add all the numbers together, and all the variables

6x^2-540x+2=0

a = 6; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·6·2
Δ = 291552
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:

$\sqrt{\Delta}=\sqrt{291552}=\sqrt{16*18222}=\sqrt{16}*\sqrt{18222}=4\sqrt{18222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-4\sqrt{18222}}{2*6}=\frac{540-4\sqrt{18222}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+4\sqrt{18222}}{2*6}=\frac{540+4\sqrt{18222}}{12}
$