3x-6/x=2

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

3x-6/x=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-2x-6=0

a = 3; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·3·(-6)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*3}=\frac{2-2\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*3}=\frac{2+2\sqrt{19}}{6}
$