12-(1/5)r=2r+1

Solution for 12-(1/5)r=2r+1 equation:

12-(1/5)r=2r+1

We move all terms to the left:

12-(1/5)r-(2r+1)=0


Domain of the equation: 5)r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

-(+1/5)r-(2r+1)+12=0

We multiply parentheses

-r^2-(2r+1)+12=0

We get rid of parentheses

-r^2-2r-1+12=0

We add all the numbers together, and all the variables

-1r^2-2r+11=0

a = -1; b = -2; c = +11;
Δ = b2-4ac
Δ = -22-4·(-1)·11
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{3}}{2*-1}=\frac{2-4\sqrt{3}}{-2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{3}}{2*-1}=\frac{2+4\sqrt{3}}{-2}
$