5/x-4=8/2x-9

Solution for 5/x-4=8/2x-9 equation:

5/x-4=8/2x-9

We move all terms to the left:

5/x-4-(8/2x-9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-9)!=0

x∈R


We get rid of parentheses

5/x-8/2x+9-4=0

We calculate fractions


10x/2x^2+(-8x)/2x^2+9-4=0

We add all the numbers together, and all the variables

10x/2x^2+(-8x)/2x^2+5=0

We multiply all the terms by the denominator


10x+(-8x)+5*2x^2=0

Wy multiply elements

10x^2+10x+(-8x)=0

We get rid of parentheses

10x^2+10x-8x=0

We add all the numbers together, and all the variables

10x^2+2x=0

a = 10; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·10·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*10}=\frac{-4}{20}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*10}=\frac{0}{20}
=0
$