x-7+11/x-5=3-x+11/x-5

Solution for x-7+11/x-5=3-x+11/x-5 equation:

x-7+11/x-5=3-x+11/x-5

We move all terms to the left:

x-7+11/x-5-(3-x+11/x-5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-5)!=0

x∈R


We add all the numbers together, and all the variables

x+11/x-(-1x+11/x-2)-7-5=0

We add all the numbers together, and all the variables

x+11/x-(-1x+11/x-2)-12=0

We get rid of parentheses

x+11/x+1x-11/x+2-12=0

We multiply all the terms by the denominator


x*x+1x*x+2*x-12*x+11-11=0

We add all the numbers together, and all the variables

-10x+x*x+1x*x=0

Wy multiply elements

x^2+x^2-10x=0

We add all the numbers together, and all the variables

2x^2-10x=0

a = 2; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·2·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*2}=\frac{20}{4}
=5
$