6x+2(x+4)=1/3x+2

Solution for 6x+2(x+4)=1/3x+2 equation:

6x+2(x+4)=1/3x+2

We move all terms to the left:

6x+2(x+4)-(1/3x+2)=0


Domain of the equation: 3x+2)!=0

x∈R


We multiply parentheses

6x+2x-(1/3x+2)+8=0

We get rid of parentheses

6x+2x-1/3x-2+8=0

We multiply all the terms by the denominator


6x*3x+2x*3x-2*3x+8*3x-1=0

Wy multiply elements

18x^2+6x^2-6x+24x-1=0

We add all the numbers together, and all the variables

24x^2+18x-1=0

a = 24; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·24·(-1)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{105}}{2*24}=\frac{-18-2\sqrt{105}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{105}}{2*24}=\frac{-18+2\sqrt{105}}{48}
$