5/x-9=2x

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

5/x-9=2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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