3x-6/2=6/x+2

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

3x-6/2=6/x+2

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-6/x-2-3=0

We multiply all the terms by the denominator


3x*x-2*x-3*x-6=0

We add all the numbers together, and all the variables

-5x+3x*x-6=0

Wy multiply elements

3x^2-5x-6=0

a = 3; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·3·(-6)
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{-(-5)-\sqrt{97}}{2*3}=\frac{5-\sqrt{97}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*3}=\frac{5+\sqrt{97}}{6}
$