2r=1/4r+4

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

2r=1/4r+4

We move all terms to the left:

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


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

r∈R


We get rid of parentheses

2r-1/4r-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

8r^2-16r-1=0

a = 8; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·8·(-1)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*8}=\frac{16-12\sqrt{2}}{16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*8}=\frac{16+12\sqrt{2}}{16}
$