3x+2/x-6=5

Solution for 3x+2/x-6=5 equation:

3x+2/x-6=5

We move all terms to the left:

3x+2/x-6-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/x-11=0

We multiply all the terms by the denominator


3x*x-11*x+2=0

We add all the numbers together, and all the variables

-11x+3x*x+2=0

Wy multiply elements

3x^2-11x+2=0

a = 3; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·3·2
Δ = 97
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{97}}{2*3}=\frac{11-\sqrt{97}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*3}=\frac{11+\sqrt{97}}{6}
$