X-4/3x-2=2

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

X-4/3X-2=2

We move all terms to the left:

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


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-4/3X-4=0

We multiply all the terms by the denominator


X*3X-4*3X-4=0

Wy multiply elements

3X^2-12X-4=0

a = 3; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·3·(-4)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*3}=\frac{12-8\sqrt{3}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*3}=\frac{12+8\sqrt{3}}{6}
$