2/3x+(x-12)+x=180

Solution for 2/3x+(x-12)+x=180 equation:

2/3x+(x-12)+x=180

We move all terms to the left:

2/3x+(x-12)+x-(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

x+2/3x+(x-12)-180=0

We get rid of parentheses

x+2/3x+x-12-180=0

We multiply all the terms by the denominator


x*3x+x*3x-12*3x-180*3x+2=0

Wy multiply elements

3x^2+3x^2-36x-540x+2=0

We add all the numbers together, and all the variables

6x^2-576x+2=0

a = 6; b = -576; c = +2;
Δ = b2-4ac
Δ = -5762-4·6·2
Δ = 331728
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:

$\sqrt{\Delta}=\sqrt{331728}=\sqrt{16*20733}=\sqrt{16}*\sqrt{20733}=4\sqrt{20733}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-576)-4\sqrt{20733}}{2*6}=\frac{576-4\sqrt{20733}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-576)+4\sqrt{20733}}{2*6}=\frac{576+4\sqrt{20733}}{12}
$