2+3x-2/x=8

Solution for 2+3x-2/x=8 equation:

2+3x-2/x=8

We move all terms to the left:

2+3x-2/x-(8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-2/x-6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-6x-2=0

a = 3; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·3·(-2)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*3}=\frac{6-2\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*3}=\frac{6+2\sqrt{15}}{6}
$