3x-9=1/x+2

Solution for 3x-9=1/x+2 equation:

3x-9=1/x+2

We move all terms to the left:

3x-9-(1/x+2)=0


Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

3x-1/x-2-9=0

We multiply all the terms by the denominator


3x*x-2*x-9*x-1=0

We add all the numbers together, and all the variables

-11x+3x*x-1=0

Wy multiply elements

3x^2-11x-1=0

a = 3; b = -11; c = -1;
Δ = b2-4ac
Δ = -112-4·3·(-1)
Δ = 133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{133}}{2*3}=\frac{11-\sqrt{133}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{133}}{2*3}=\frac{11+\sqrt{133}}{6}
$