3x-2/x+4=2

Solution for 3x-2/x+4=2 equation:

3x-2/x+4=2

We move all terms to the left:

3x-2/x+4-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-2/x+2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x+3x*x-2=0

Wy multiply elements

3x^2+2x-2=0

a = 3; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·3·(-2)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*3}=\frac{-2-2\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*3}=\frac{-2+2\sqrt{7}}{6}
$