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

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

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

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


x*3x+2*3x-180*3x+1=0

Wy multiply elements

3x^2+6x-540x+1=0

We add all the numbers together, and all the variables

3x^2-534x+1=0

a = 3; b = -534; c = +1;
Δ = b2-4ac
Δ = -5342-4·3·1
Δ = 285144
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:

$\sqrt{\Delta}=\sqrt{285144}=\sqrt{47524*6}=\sqrt{47524}*\sqrt{6}=218\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-534)-218\sqrt{6}}{2*3}=\frac{534-218\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-534)+218\sqrt{6}}{2*3}=\frac{534+218\sqrt{6}}{6}
$