X+2/x+x=74/x

Solution for X+2/x+x=74/x equation:

X+2/X+X=74/X

We move all terms to the left:

X+2/X+X-(74/X)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+2/X+X-(+74/X)=0

We add all the numbers together, and all the variables

2X+2/X-(+74/X)=0

We get rid of parentheses

2X+2/X-74/X=0

We multiply all the terms by the denominator


2X*X+2-74=0

We add all the numbers together, and all the variables

2X*X-72=0

Wy multiply elements

2X^2-72=0

a = 2; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·2·(-72)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*2}=\frac{-24}{4}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*2}=\frac{24}{4}
=6
$