2r-8=1/4r

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

2r-8=1/4r

We move all terms to the left:

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


Domain of the equation: 4r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2r-1/4r-8=0

We multiply all the terms by the denominator


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

Wy multiply elements

8r^2-32r-1=0

a = 8; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·8·(-1)
Δ = 1056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{66}}{2*8}=\frac{32-4\sqrt{66}}{16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{66}}{2*8}=\frac{32+4\sqrt{66}}{16}
$