(1/3x)+x+(x-44)=180

Solution for (1/3x)+x+(x-44)=180 equation:

(1/3x)+x+(x-44)=180

We move all terms to the left:

(1/3x)+x+(x-44)-(180)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3x)+x+(x-44)-180=0

We add all the numbers together, and all the variables

x+(+1/3x)+(x-44)-180=0

We get rid of parentheses

x+1/3x+x-44-180=0

We multiply all the terms by the denominator


x*3x+x*3x-44*3x-180*3x+1=0

Wy multiply elements

3x^2+3x^2-132x-540x+1=0

We add all the numbers together, and all the variables

6x^2-672x+1=0

a = 6; b = -672; c = +1;
Δ = b2-4ac
Δ = -6722-4·6·1
Δ = 451560
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:

$\sqrt{\Delta}=\sqrt{451560}=\sqrt{4*112890}=\sqrt{4}*\sqrt{112890}=2\sqrt{112890}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-2\sqrt{112890}}{2*6}=\frac{672-2\sqrt{112890}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+2\sqrt{112890}}{2*6}=\frac{672+2\sqrt{112890}}{12}
$