5x+9-2/x=0

Solution for 5x+9-2/x=0 equation:

5x+9-2/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

9x+5x*x-2=0

Wy multiply elements

5x^2+9x-2=0

a = 5; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·5·(-2)
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*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*5}=\frac{2}{10}
=1/5
$