x-9/2x+6=x+5/x

Solution for x-9/2x+6=x+5/x equation:

x-9/2x+6=x+5/x

We move all terms to the left:

x-9/2x+6-(x+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

x-9/2x-(+x+5/x)+6=0

We get rid of parentheses

x-9/2x-x-5/x+6=0

We calculate fractions


x-x+(-9x)/2x^2+(-10x)/2x^2+6=0

We add all the numbers together, and all the variables

(-9x)/2x^2+(-10x)/2x^2+6=0

We multiply all the terms by the denominator


(-9x)+(-10x)+6*2x^2=0

Wy multiply elements

12x^2+(-9x)+(-10x)=0

We get rid of parentheses

12x^2-9x-10x=0

We add all the numbers together, and all the variables

12x^2-19x=0

a = 12; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·12·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*12}=\frac{38}{24}
=1+7/12
$