1/x+1/x+11=23/11x+33

Solution for 1/x+1/x+11=23/11x+33 equation:

1/x+1/x+11=23/11x+33

We move all terms to the left:

1/x+1/x+11-(23/11x+33)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 11x+33)!=0

x∈R


We get rid of parentheses

1/x+1/x-23/11x-33+11=0

We calculate fractions


(11x+1)/11x^2+(-23x)/11x^2-33+11=0

We add all the numbers together, and all the variables

(11x+1)/11x^2+(-23x)/11x^2-22=0

We multiply all the terms by the denominator


(11x+1)+(-23x)-22*11x^2=0

Wy multiply elements

-242x^2+(11x+1)+(-23x)=0

We get rid of parentheses

-242x^2+11x-23x+1=0

We add all the numbers together, and all the variables

-242x^2-12x+1=0

a = -242; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-242)·1
Δ = 1112
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:

$\sqrt{\Delta}=\sqrt{1112}=\sqrt{4*278}=\sqrt{4}*\sqrt{278}=2\sqrt{278}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{278}}{2*-242}=\frac{12-2\sqrt{278}}{-484}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{278}}{2*-242}=\frac{12+2\sqrt{278}}{-484}
$