5x+12/3x+x=180

Solution for 5x+12/3x+x=180 equation:

5x+12/3x+x=180

We move all terms to the left:

5x+12/3x+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

6x+12/3x-180=0

We multiply all the terms by the denominator


6x*3x-180*3x+12=0

Wy multiply elements

18x^2-540x+12=0

a = 18; b = -540; c = +12;
Δ = b2-4ac
Δ = -5402-4·18·12
Δ = 290736
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:

$\sqrt{\Delta}=\sqrt{290736}=\sqrt{144*2019}=\sqrt{144}*\sqrt{2019}=12\sqrt{2019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-12\sqrt{2019}}{2*18}=\frac{540-12\sqrt{2019}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+12\sqrt{2019}}{2*18}=\frac{540+12\sqrt{2019}}{36}
$