X+x+2/x+4=66-x

Solution for X+x+2/x+4=66-x equation:

X+X+2/X+4=66-X

We move all terms to the left:

X+X+2/X+4-(66-X)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+X+2/X-(-1X+66)+4=0

We add all the numbers together, and all the variables

2X+2/X-(-1X+66)+4=0

We get rid of parentheses

2X+2/X+1X-66+4=0

We multiply all the terms by the denominator


2X*X+1X*X-66*X+4*X+2=0

We add all the numbers together, and all the variables

-62X+2X*X+1X*X+2=0

Wy multiply elements

2X^2+X^2-62X+2=0

We add all the numbers together, and all the variables

3X^2-62X+2=0

a = 3; b = -62; c = +2;
Δ = b2-4ac
Δ = -622-4·3·2
Δ = 3820
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:

$\sqrt{\Delta}=\sqrt{3820}=\sqrt{4*955}=\sqrt{4}*\sqrt{955}=2\sqrt{955}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-2\sqrt{955}}{2*3}=\frac{62-2\sqrt{955}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+2\sqrt{955}}{2*3}=\frac{62+2\sqrt{955}}{6}
$