3x-2/x-4=4

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

3x-2/x-4=4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-2/x-8=0

We multiply all the terms by the denominator


3x*x-8*x-2=0

We add all the numbers together, and all the variables

-8x+3x*x-2=0

Wy multiply elements

3x^2-8x-2=0

a = 3; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·3·(-2)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*3}=\frac{8-2\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*3}=\frac{8+2\sqrt{22}}{6}
$