61/2x=x

Solution for 61/2x=x equation:

61/2x=x

We move all terms to the left:

61/2x-(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+61/2x=0

We multiply all the terms by the denominator


-1x*2x+61=0

Wy multiply elements

-2x^2+61=0

a = -2; b = 0; c = +61;
Δ = b2-4ac
Δ = 02-4·(-2)·61
Δ = 488
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:

$\sqrt{\Delta}=\sqrt{488}=\sqrt{4*122}=\sqrt{4}*\sqrt{122}=2\sqrt{122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{122}}{2*-2}=\frac{0-2\sqrt{122}}{-4}
=-\frac{2\sqrt{122}}{-4}
=-\frac{\sqrt{122}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{122}}{2*-2}=\frac{0+2\sqrt{122}}{-4}
=\frac{2\sqrt{122}}{-4}
=\frac{\sqrt{122}}{-2}
$