8/x=9/2x-1

Solution for 8/x=9/2x-1 equation:

8/x=9/2x-1

We move all terms to the left:

8/x-(9/2x-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

8/x-9/2x+1=0

We calculate fractions


16x/2x^2+(-9x)/2x^2+1=0

We multiply all the terms by the denominator


16x+(-9x)+1*2x^2=0

Wy multiply elements

2x^2+16x+(-9x)=0

We get rid of parentheses

2x^2+16x-9x=0

We add all the numbers together, and all the variables

2x^2+7x=0

a = 2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*2}=\frac{0}{4}
=0
$