1/3x+2=3x+8

Solution for 1/3x+2=3x+8 equation:

1/3x+2=3x+8

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2-24x+6x+1=0

We add all the numbers together, and all the variables

-9x^2-18x+1=0

a = -9; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-9)·1
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{10}}{2*-9}=\frac{18-6\sqrt{10}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{10}}{2*-9}=\frac{18+6\sqrt{10}}{-18}
$