(11/x+2)-(3x+2/x)=0

Solution for (11/x+2)-(3x+2/x)=0 equation:

(11/x+2)-(3x+2/x)=0


Domain of the equation: x+2)!=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

(11/x+2)-(+3x+2/x)=0

We get rid of parentheses

11/x-3x-2/x+2=0

We multiply all the terms by the denominator


-3x*x+2*x+11-2=0

We add all the numbers together, and all the variables

2x-3x*x+9=0

Wy multiply elements

-3x^2+2x+9=0

a = -3; b = 2; c = +9;
Δ = b2-4ac
Δ = 22-4·(-3)·9
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{7}}{2*-3}=\frac{-2-4\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{7}}{2*-3}=\frac{-2+4\sqrt{7}}{-6}
$