X-4/2x+9=x+6/x

Solution for X-4/2x+9=x+6/x equation:

X-4/2X+9=X+6/X

We move all terms to the left:

X-4/2X+9-(X+6/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-4/2X-(+X+6/X)+9=0

We get rid of parentheses

X-4/2X-X-6/X+9=0

We calculate fractions


X-X+(-4X)/2X^2+(-12X)/2X^2+9=0

We add all the numbers together, and all the variables

(-4X)/2X^2+(-12X)/2X^2+9=0

We multiply all the terms by the denominator


(-4X)+(-12X)+9*2X^2=0

Wy multiply elements

18X^2+(-4X)+(-12X)=0

We get rid of parentheses

18X^2-4X-12X=0

We add all the numbers together, and all the variables

18X^2-16X=0

a = 18; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·18·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*18}=\frac{0}{36}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*18}=\frac{32}{36}
=8/9
$