12=2000/12*r

Solution for 12=2000/12*r equation:

12=2000/12*r

We move all terms to the left:

12-(2000/12*r)=0


Domain of the equation: 12*r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

-(+2000/12*r)+12=0

We get rid of parentheses

-2000/12*r+12=0

We multiply all the terms by the denominator


12*12*r-2000=0

Wy multiply elements

144r*r-2000=0

Wy multiply elements

144r^2-2000=0

a = 144; b = 0; c = -2000;
Δ = b2-4ac
Δ = 02-4·144·(-2000)
Δ = 1152000
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:

$\sqrt{\Delta}=\sqrt{1152000}=\sqrt{230400*5}=\sqrt{230400}*\sqrt{5}=480\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-480\sqrt{5}}{2*144}=\frac{0-480\sqrt{5}}{288}
=-\frac{480\sqrt{5}}{288}
=-\frac{5\sqrt{5}}{3}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+480\sqrt{5}}{2*144}=\frac{0+480\sqrt{5}}{288}
=\frac{480\sqrt{5}}{288}
=\frac{5\sqrt{5}}{3}
$