3x+2=9/x

Solution for 3x+2=9/x equation:

3x+2=9/x

We move all terms to the left:

3x+2-(9/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

3x-(+9/x)+2=0

We get rid of parentheses

3x-9/x+2=0

We multiply all the terms by the denominator


3x*x+2*x-9=0

We add all the numbers together, and all the variables

2x+3x*x-9=0

Wy multiply elements

3x^2+2x-9=0

a = 3; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·3·(-9)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{7}}{2*3}=\frac{-2-4\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{7}}{2*3}=\frac{-2+4\sqrt{7}}{6}
$