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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


16x/2x^2+(-8x)/2x^2-5-9=0

We add all the numbers together, and all the variables

16x/2x^2+(-8x)/2x^2-14=0

We multiply all the terms by the denominator


16x+(-8x)-14*2x^2=0

Wy multiply elements

-28x^2+16x+(-8x)=0

We get rid of parentheses

-28x^2+16x-8x=0

We add all the numbers together, and all the variables

-28x^2+8x=0

a = -28; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-28)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-28}=\frac{-16}{-56}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-28}=\frac{0}{-56}
=0
$