3x-4-6/x=12

Solution for 3x-4-6/x=12 equation:

3x-4-6/x=12

We move all terms to the left:

3x-4-6/x-(12)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-6/x-16=0

We multiply all the terms by the denominator


3x*x-16*x-6=0

We add all the numbers together, and all the variables

-16x+3x*x-6=0

Wy multiply elements

3x^2-16x-6=0

a = 3; b = -16; c = -6;
Δ = b2-4ac
Δ = -162-4·3·(-6)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{82}}{2*3}=\frac{16-2\sqrt{82}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{82}}{2*3}=\frac{16+2\sqrt{82}}{6}
$