6+x=8/3x

Solution for 6+x=8/3x equation:

6+x=8/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-8/3x+6=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+18x-8=0

a = 3; b = 18; c = -8;
Δ = b2-4ac
Δ = 182-4·3·(-8)
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*3}=\frac{-18-2\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{105}}{2*3}=\frac{-18+2\sqrt{105}}{6}
$