x+x-4+2/3x=180

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Solution for x+x-4+2/3x=180 equation: 



x+x-4+2/3x=180

We move all terms to the left:

x+x-4+2/3x-(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-184=0

We multiply all the terms by the denominator


2x*3x-184*3x+2=0

Wy multiply elements

6x^2-552x+2=0

a = 6; b = -552; c = +2;
Δ = b2-4ac
Δ = -5522-4·6·2
Δ = 304656
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:


$\sqrt{\Delta}=\sqrt{304656}=\sqrt{16*19041}=\sqrt{16}*\sqrt{19041}=4\sqrt{19041}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-552)-4\sqrt{19041}}{2*6}=\frac{552-4\sqrt{19041}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-552)+4\sqrt{19041}}{2*6}=\frac{552+4\sqrt{19041}}{12}
$

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