1/x+x=180

Solution for 1/x+x=180 equation:

1/x+x=180

We move all terms to the left:

1/x+x-(180)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-180=0

We multiply all the terms by the denominator


x*x-180*x+1=0

We add all the numbers together, and all the variables

-180x+x*x+1=0

Wy multiply elements

x^2-180x+1=0

a = 1; b = -180; c = +1;
Δ = b2-4ac
Δ = -1802-4·1·1
Δ = 32396
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:

$\sqrt{\Delta}=\sqrt{32396}=\sqrt{4*8099}=\sqrt{4}*\sqrt{8099}=2\sqrt{8099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8099}}{2*1}=\frac{180-2\sqrt{8099}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8099}}{2*1}=\frac{180+2\sqrt{8099}}{2}
$