x/3x-2+x=6

Solution for x/3x-2+x=6 equation:

x/3x-2+x=6

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+x/3x-8=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2+x-24x=0

We add all the numbers together, and all the variables

3x^2-23x=0

a = 3; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·3·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*3}=\frac{46}{6}
=7+2/3
$