9/2x=10-8/x=

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

9/2x=10-8/x=

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


9x/2x^2+16x/2x^2-10=0

We multiply all the terms by the denominator


9x+16x-10*2x^2=0

We add all the numbers together, and all the variables

25x-10*2x^2=0

Wy multiply elements

-20x^2+25x=0

a = -20; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-20)·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*-20}=\frac{-50}{-40}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-20}=\frac{0}{-40}
=0
$