6/2x-8=-5/x+9

Solution for 6/2x-8=-5/x+9 equation:

6/2x-8=-5/x+9

We move all terms to the left:

6/2x-8-(-5/x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+9)!=0

x∈R


We get rid of parentheses

6/2x+5/x-9-8=0

We calculate fractions


6x/2x^2+10x/2x^2-9-8=0

We add all the numbers together, and all the variables

6x/2x^2+10x/2x^2-17=0

We multiply all the terms by the denominator


6x+10x-17*2x^2=0

We add all the numbers together, and all the variables

16x-17*2x^2=0

Wy multiply elements

-34x^2+16x=0

a = -34; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-34)·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*-34}=\frac{-32}{-68}
=8/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-34}=\frac{0}{-68}
=0
$