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

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

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

We move all terms to the left:

3x+1/3x+x-44-(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-224=0

We multiply all the terms by the denominator


4x*3x-224*3x+1=0

Wy multiply elements

12x^2-672x+1=0

a = 12; b = -672; c = +1;
Δ = b2-4ac
Δ = -6722-4·12·1
Δ = 451536
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:

$\sqrt{\Delta}=\sqrt{451536}=\sqrt{16*28221}=\sqrt{16}*\sqrt{28221}=4\sqrt{28221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-4\sqrt{28221}}{2*12}=\frac{672-4\sqrt{28221}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+4\sqrt{28221}}{2*12}=\frac{672+4\sqrt{28221}}{24}
$