10/5x-9=9/2x-8

Solution for 10/5x-9=9/2x-8 equation:

10/5x-9=9/2x-8

We move all terms to the left:

10/5x-9-(9/2x-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-8)!=0

x∈R


We get rid of parentheses

10/5x-9/2x+8-9=0

We calculate fractions


20x/10x^2+(-45x)/10x^2+8-9=0

We add all the numbers together, and all the variables

20x/10x^2+(-45x)/10x^2-1=0

We multiply all the terms by the denominator


20x+(-45x)-1*10x^2=0

Wy multiply elements

-10x^2+20x+(-45x)=0

We get rid of parentheses

-10x^2+20x-45x=0

We add all the numbers together, and all the variables

-10x^2-25x=0

a = -10; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-10)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-10}=\frac{50}{-20}
=-2+1/2
$