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

Solution for 2x-12/(6-x)=0 equation:

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


Domain of the equation: (6-x)!=0

We move all terms containing x to the left, all other terms to the right

-x!=-6

x!=-6/-1

x!=+6

x∈R


We add all the numbers together, and all the variables

2x-12/(-1x+6)=0

We multiply all the terms by the denominator


2x*(-1x+6)-12=0

We multiply parentheses

-2x^2+12x-12=0

a = -2; b = 12; c = -12;
Δ = b2-4ac
Δ = 122-4·(-2)·(-12)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*-2}=\frac{-12-4\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*-2}=\frac{-12+4\sqrt{3}}{-4}
$