2x+1+x+3/2x=180

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Solution for 2x+1+x+3/2x=180 equation: 



2x+1+x+3/2x=180

We move all terms to the left:

2x+1+x+3/2x-(180)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We add all the numbers together, and all the variables

3x+3/2x-179=0

We multiply all the terms by the denominator


3x*2x-179*2x+3=0

Wy multiply elements

6x^2-358x+3=0

a = 6; b = -358; c = +3;
Δ = b2-4ac
Δ = -3582-4·6·3
Δ = 128092
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:


$\sqrt{\Delta}=\sqrt{128092}=\sqrt{4*32023}=\sqrt{4}*\sqrt{32023}=2\sqrt{32023}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-358)-2\sqrt{32023}}{2*6}=\frac{358-2\sqrt{32023}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-358)+2\sqrt{32023}}{2*6}=\frac{358+2\sqrt{32023}}{12}
$

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