9x+3=1/x

Solution for 9x+3=1/x equation:

9x+3=1/x

We move all terms to the left:

9x+3-(1/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

9x-(+1/x)+3=0

We get rid of parentheses

9x-1/x+3=0

We multiply all the terms by the denominator


9x*x+3*x-1=0

We add all the numbers together, and all the variables

3x+9x*x-1=0

Wy multiply elements

9x^2+3x-1=0

a = 9; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·9·(-1)
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{5}}{2*9}=\frac{-3-3\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{5}}{2*9}=\frac{-3+3\sqrt{5}}{18}
$