(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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


x*x+(x+2)-74=0

Wy multiply elements

x^2+(x+2)-74=0

We get rid of parentheses

x^2+x+2-74=0

We add all the numbers together, and all the variables

x^2+x-72=0

a = 1; b = 1; c = -72;
Δ = b2-4ac
Δ = 12-4·1·(-72)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*1}=\frac{16}{2}
=8
$