X+2x+2/3x=120

Solution for X+2x+2/3x=120 equation:

X+2X+2/3X=120

We move all terms to the left:

X+2X+2/3X-(120)=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-120=0

We multiply all the terms by the denominator


3X*3X-120*3X+2=0

Wy multiply elements

9X^2-360X+2=0

a = 9; b = -360; c = +2;
Δ = b2-4ac
Δ = -3602-4·9·2
Δ = 129528
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:

$\sqrt{\Delta}=\sqrt{129528}=\sqrt{36*3598}=\sqrt{36}*\sqrt{3598}=6\sqrt{3598}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-6\sqrt{3598}}{2*9}=\frac{360-6\sqrt{3598}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+6\sqrt{3598}}{2*9}=\frac{360+6\sqrt{3598}}{18}
$