3x-(4/x)=12

Solution for 3x-(4/x)=12 equation:

3x-(4/x)=12

We move all terms to the left:

3x-(4/x)-(12)=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-(+4/x)-12=0

We get rid of parentheses

3x-4/x-12=0

We multiply all the terms by the denominator


3x*x-12*x-4=0

We add all the numbers together, and all the variables

-12x+3x*x-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}
$