12-1/2x=x

Solution for 12-1/2x=x equation:

12-1/2x=x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-1/2x+12=0

We multiply all the terms by the denominator


-1x*2x+12*2x-1=0

Wy multiply elements

-2x^2+24x-1=0

a = -2; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-2)·(-1)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{142}}{2*-2}=\frac{-24-2\sqrt{142}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{142}}{2*-2}=\frac{-24+2\sqrt{142}}{-4}
$