3*x+3/x=180

Solution for 3*x+3/x=180 equation:

3x+3/x=180

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-180x+3=0

a = 3; b = -180; c = +3;
Δ = b2-4ac
Δ = -1802-4·3·3
Δ = 32364
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:

$\sqrt{\Delta}=\sqrt{32364}=\sqrt{36*899}=\sqrt{36}*\sqrt{899}=6\sqrt{899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-6\sqrt{899}}{2*3}=\frac{180-6\sqrt{899}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+6\sqrt{899}}{2*3}=\frac{180+6\sqrt{899}}{6}
$