2x+1/x+38=180

Solution for 2x+1/x+38=180 equation:

2x+1/x+38=180

We move all terms to the left:

2x+1/x+38-(180)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/x-142=0

We multiply all the terms by the denominator


2x*x-142*x+1=0

We add all the numbers together, and all the variables

-142x+2x*x+1=0

Wy multiply elements

2x^2-142x+1=0

a = 2; b = -142; c = +1;
Δ = b2-4ac
Δ = -1422-4·2·1
Δ = 20156
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:

$\sqrt{\Delta}=\sqrt{20156}=\sqrt{4*5039}=\sqrt{4}*\sqrt{5039}=2\sqrt{5039}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-142)-2\sqrt{5039}}{2*2}=\frac{142-2\sqrt{5039}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-142)+2\sqrt{5039}}{2*2}=\frac{142+2\sqrt{5039}}{4}
$