1/2r=1/4r+8

Solution for 1/2r=1/4r+8 equation:

1/2r=1/4r+8

We move all terms to the left:

1/2r-(1/4r+8)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 4r+8)!=0

r∈R


We get rid of parentheses

1/2r-1/4r-8=0

We calculate fractions


4r/8r^2+(-2r)/8r^2-8=0

We multiply all the terms by the denominator


4r+(-2r)-8*8r^2=0

Wy multiply elements

-64r^2+4r+(-2r)=0

We get rid of parentheses

-64r^2+4r-2r=0

We add all the numbers together, and all the variables

-64r^2+2r=0

a = -64; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-64)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-64}=\frac{-4}{-128}
=1/32
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-64}=\frac{0}{-128}
=0
$