X/2x-32x=1

Solution for X/2x-32x=1 equation:

X/2X-32X=1

We move all terms to the left:

X/2X-32X-(1)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

-32X+X/2X-1=0

We multiply all the terms by the denominator


-32X*2X+X-1*2X=0

We add all the numbers together, and all the variables

X-32X*2X-1*2X=0

Wy multiply elements

-64X^2+X-2X=0

We add all the numbers together, and all the variables

-64X^2-1X=0

a = -64; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-64)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-64}=\frac{0}{-128}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-64}=\frac{2}{-128}
=-1/64
$