x+40+3x-60+1/3x+20=180

Solution for x+40+3x-60+1/3x+20=180 equation:

x+40+3x-60+1/3x+20=180

We move all terms to the left:

x+40+3x-60+1/3x+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

4x+1/3x-180=0

We multiply all the terms by the denominator


4x*3x-180*3x+1=0

Wy multiply elements

12x^2-540x+1=0

a = 12; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·12·1
Δ = 291552
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:

$\sqrt{\Delta}=\sqrt{291552}=\sqrt{16*18222}=\sqrt{16}*\sqrt{18222}=4\sqrt{18222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-4\sqrt{18222}}{2*12}=\frac{540-4\sqrt{18222}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+4\sqrt{18222}}{2*12}=\frac{540+4\sqrt{18222}}{24}
$