(2/x)+(x+30)=180

Solution for (2/x)+(x+30)=180 equation:

(2/x)+(x+30)=180

We move all terms to the left:

(2/x)+(x+30)-(180)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/x)+(x+30)-180=0

We get rid of parentheses

2/x+x+30-180=0

We multiply all the terms by the denominator


x*x+30*x-180*x+2=0

We add all the numbers together, and all the variables

-150x+x*x+2=0

Wy multiply elements

x^2-150x+2=0

a = 1; b = -150; c = +2;
Δ = b2-4ac
Δ = -1502-4·1·2
Δ = 22492
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:

$\sqrt{\Delta}=\sqrt{22492}=\sqrt{4*5623}=\sqrt{4}*\sqrt{5623}=2\sqrt{5623}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5623}}{2*1}=\frac{150-2\sqrt{5623}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5623}}{2*1}=\frac{150+2\sqrt{5623}}{2}
$