2x-6+x+4+2/x+2/x=180

Solution for 2x-6+x+4+2/x+2/x=180 equation:

2x-6+x+4+2/x+2/x=180

We move all terms to the left:

2x-6+x+4+2/x+2/x-(180)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/x+2/x-182=0

We multiply all the terms by the denominator


3x*x-182*x+2+2=0

We add all the numbers together, and all the variables

-182x+3x*x+4=0

Wy multiply elements

3x^2-182x+4=0

a = 3; b = -182; c = +4;
Δ = b2-4ac
Δ = -1822-4·3·4
Δ = 33076
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:

$\sqrt{\Delta}=\sqrt{33076}=\sqrt{4*8269}=\sqrt{4}*\sqrt{8269}=2\sqrt{8269}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182)-2\sqrt{8269}}{2*3}=\frac{182-2\sqrt{8269}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182)+2\sqrt{8269}}{2*3}=\frac{182+2\sqrt{8269}}{6}
$