11/2x-1=5/x

Solution for 11/2x-1=5/x equation:

11/2x-1=5/x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

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

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

We get rid of parentheses

11/2x-5/x-1=0

We calculate fractions


11x/2x^2+(-10x)/2x^2-1=0

We multiply all the terms by the denominator


11x+(-10x)-1*2x^2=0

Wy multiply elements

-2x^2+11x+(-10x)=0

We get rid of parentheses

-2x^2+11x-10x=0

We add all the numbers together, and all the variables

-2x^2+x=0

a = -2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-2)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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