9=2x-5/x

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

9=2x-5/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x+5/x+9=0

We multiply all the terms by the denominator


-2x*x+9*x+5=0

We add all the numbers together, and all the variables

9x-2x*x+5=0

Wy multiply elements

-2x^2+9x+5=0

a = -2; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·(-2)·5
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*-2}=\frac{2}{-4}
=-1/2
$