3x-4=2/x

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

3x-4=2/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-2/x-4=0

We multiply all the terms by the denominator


3x*x-4*x-2=0

We add all the numbers together, and all the variables

-4x+3x*x-2=0

Wy multiply elements

3x^2-4x-2=0

a = 3; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·3·(-2)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*3}=\frac{4-2\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*3}=\frac{4+2\sqrt{10}}{6}
$