R+6/2r-1=2r+1/2r

Solution for R+6/2r-1=2r+1/2r equation:

+6/2R-1=2R+1/2R

We move all terms to the left:

+6/2R-1-(2R+1/2R)=0


Domain of the equation: 2R!=0

R!=0/2

R!=0

R∈R



Domain of the equation: 2R)!=0

R!=0/1

R!=0

R∈R


We add all the numbers together, and all the variables

6/2R-(+2R+1/2R)-1=0

We get rid of parentheses

6/2R-2R-1/2R-1=0

We multiply all the terms by the denominator


-2R*2R-1*2R+6-1=0

We add all the numbers together, and all the variables

-2R*2R-1*2R+5=0

Wy multiply elements

-4R^2-2R+5=0

a = -4; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-4)·5
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*-4}=\frac{2-2\sqrt{21}}{-8}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*-4}=\frac{2+2\sqrt{21}}{-8}
$