9/x+1=2x+2/x

Solution for 9/x+1=2x+2/x equation:

9/x+1=2x+2/x

We move all terms to the left:

9/x+1-(2x+2/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

9/x-(+2x+2/x)+1=0

We get rid of parentheses

9/x-2x-2/x+1=0

We multiply all the terms by the denominator


-2x*x+1*x+9-2=0

We add all the numbers together, and all the variables

x-2x*x+7=0

Wy multiply elements

-2x^2+x+7=0

a = -2; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-2)·7
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{57}}{2*-2}=\frac{-1-\sqrt{57}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*-2}=\frac{-1+\sqrt{57}}{-4}
$