12=2r+1/3r

Solution for 12=2r+1/3r equation:

12=2r+1/3r

We move all terms to the left:

12-(2r+1/3r)=0


Domain of the equation: 3r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

-(+2r+1/3r)+12=0

We get rid of parentheses

-2r-1/3r+12=0

We multiply all the terms by the denominator


-2r*3r+12*3r-1=0

Wy multiply elements

-6r^2+36r-1=0

a = -6; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-6)·(-1)
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{318}}{2*-6}=\frac{-36-2\sqrt{318}}{-12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{318}}{2*-6}=\frac{-36+2\sqrt{318}}{-12}
$