81-4x=1/2x

Solution for 81-4x=1/2x equation:

81-4x=1/2x

We move all terms to the left:

81-4x-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-(+1/2x)+81=0

We get rid of parentheses

-4x-1/2x+81=0

We multiply all the terms by the denominator


-4x*2x+81*2x-1=0

Wy multiply elements

-8x^2+162x-1=0

a = -8; b = 162; c = -1;
Δ = b2-4ac
Δ = 1622-4·(-8)·(-1)
Δ = 26212
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:

$\sqrt{\Delta}=\sqrt{26212}=\sqrt{4*6553}=\sqrt{4}*\sqrt{6553}=2\sqrt{6553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-2\sqrt{6553}}{2*-8}=\frac{-162-2\sqrt{6553}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+2\sqrt{6553}}{2*-8}=\frac{-162+2\sqrt{6553}}{-16}
$