2x/x^2-9=0

Solution for 2x/x^2-9=0 equation:

2x/x^2-9=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


2x-9*x^2=0

We add all the numbers together, and all the variables

-9x^2+2x=0

a = -9; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-9)·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*-9}=\frac{-4}{-18}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-9}=\frac{0}{-18}
=0
$