x+3x+1/3x-22=180

Solution for x+3x+1/3x-22=180 equation:

x+3x+1/3x-22=180

We move all terms to the left:

x+3x+1/3x-22-(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

4x+1/3x-202=0

We multiply all the terms by the denominator


4x*3x-202*3x+1=0

Wy multiply elements

12x^2-606x+1=0

a = 12; b = -606; c = +1;
Δ = b2-4ac
Δ = -6062-4·12·1
Δ = 367188
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:

$\sqrt{\Delta}=\sqrt{367188}=\sqrt{4*91797}=\sqrt{4}*\sqrt{91797}=2\sqrt{91797}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-606)-2\sqrt{91797}}{2*12}=\frac{606-2\sqrt{91797}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-606)+2\sqrt{91797}}{2*12}=\frac{606+2\sqrt{91797}}{24}
$