2/3x+.132x+6=x

Solution for 2/3x+.132x+6=x equation:

2/3x+.132x+6=x

We move all terms to the left:

2/3x+.132x+6-(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

-0.868x+2/3x+6=0

We multiply all the terms by the denominator


-(0.868x)*3x+6*3x+2=0

We add all the numbers together, and all the variables

-(+0.868x)*3x+6*3x+2=0

We multiply parentheses

-0x^2+6*3x+2=0

Wy multiply elements

-0x^2+18x+2=0

We add all the numbers together, and all the variables

-1x^2+18x+2=0

a = -1; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·(-1)·2
Δ = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{83}}{2*-1}=\frac{-18-2\sqrt{83}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{83}}{2*-1}=\frac{-18+2\sqrt{83}}{-2}
$