2x+x+2/3x=78

Solution for 2x+x+2/3x=78 equation:

2x+x+2/3x=78

We move all terms to the left:

2x+x+2/3x-(78)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/3x-78=0

We multiply all the terms by the denominator


3x*3x-78*3x+2=0

Wy multiply elements

9x^2-234x+2=0

a = 9; b = -234; c = +2;
Δ = b2-4ac
Δ = -2342-4·9·2
Δ = 54684
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:

$\sqrt{\Delta}=\sqrt{54684}=\sqrt{1764*31}=\sqrt{1764}*\sqrt{31}=42\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-42\sqrt{31}}{2*9}=\frac{234-42\sqrt{31}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+42\sqrt{31}}{2*9}=\frac{234+42\sqrt{31}}{18}
$