6n-12/n-2=6

Solution for 6n-12/n-2=6 equation:

6n-12/n-2=6

We move all terms to the left:

6n-12/n-2-(6)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

6n-12/n-8=0

We multiply all the terms by the denominator


6n*n-8*n-12=0

We add all the numbers together, and all the variables

-8n+6n*n-12=0

Wy multiply elements

6n^2-8n-12=0

a = 6; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·6·(-12)
Δ = 352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{22}}{2*6}=\frac{8-4\sqrt{22}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{22}}{2*6}=\frac{8+4\sqrt{22}}{12}
$