3x+x+2/3x=6

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

3x+x+2/3x=6

We move all terms to the left:

3x+x+2/3x-(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

4x+2/3x-6=0

We multiply all the terms by the denominator


4x*3x-6*3x+2=0

Wy multiply elements

12x^2-18x+2=0

a = 12; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·12·2
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{57}}{2*12}=\frac{18-2\sqrt{57}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{57}}{2*12}=\frac{18+2\sqrt{57}}{24}
$