(5+x)+(5-x)+5x+(5/x)=252

Solution for (5+x)+(5-x)+5x+(5/x)=252 equation:

(5+x)+(5-x)+5x+(5/x)=252

We move all terms to the left:

(5+x)+(5-x)+5x+(5/x)-(252)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(x+5)+(-1x+5)+5x+(+5/x)-252=0

We add all the numbers together, and all the variables

5x+(x+5)+(-1x+5)+(+5/x)-252=0

We get rid of parentheses

5x+x-1x+5/x+5+5-252=0

We multiply all the terms by the denominator


5x*x+x*x-1x*x+5*x+5*x-252*x+5=0

We add all the numbers together, and all the variables

-242x+5x*x+x*x-1x*x+5=0

Wy multiply elements

5x^2+x^2-1x^2-242x+5=0

We add all the numbers together, and all the variables

5x^2-242x+5=0

a = 5; b = -242; c = +5;
Δ = b2-4ac
Δ = -2422-4·5·5
Δ = 58464
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:

$\sqrt{\Delta}=\sqrt{58464}=\sqrt{144*406}=\sqrt{144}*\sqrt{406}=12\sqrt{406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-242)-12\sqrt{406}}{2*5}=\frac{242-12\sqrt{406}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-242)+12\sqrt{406}}{2*5}=\frac{242+12\sqrt{406}}{10}
$