2/3x+x+x+20=180

Solution for 2/3x+x+x+20=180 equation:

2/3x+x+x+20=180

We move all terms to the left:

2/3x+x+x+20-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+2/3x-160=0

We multiply all the terms by the denominator


2x*3x-160*3x+2=0

Wy multiply elements

6x^2-480x+2=0

a = 6; b = -480; c = +2;
Δ = b2-4ac
Δ = -4802-4·6·2
Δ = 230352
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:

$\sqrt{\Delta}=\sqrt{230352}=\sqrt{16*14397}=\sqrt{16}*\sqrt{14397}=4\sqrt{14397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-4\sqrt{14397}}{2*6}=\frac{480-4\sqrt{14397}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+4\sqrt{14397}}{2*6}=\frac{480+4\sqrt{14397}}{12}
$