8-6/x=12-x-2

Solution for 8-6/x=12-x-2 equation:

8-6/x=12-x-2

We move all terms to the left:

8-6/x-(12-x-2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6/x-(-1x+10)+8=0

We get rid of parentheses

-6/x+1x-10+8=0

We multiply all the terms by the denominator


1x*x-10*x+8*x-6=0

We add all the numbers together, and all the variables

-2x+1x*x-6=0

Wy multiply elements

x^2-2x-6=0

a = 1; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·1·(-6)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*1}=\frac{2-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*1}=\frac{2+2\sqrt{7}}{2}
$