18/r=2*r

Solution for 18/r=2*r equation:

18/r=2r

We move all terms to the left:

18/r-(2r)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

-2r+18/r=0

We multiply all the terms by the denominator


-2r*r+18=0

Wy multiply elements

-2r^2+18=0

a = -2; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-2)·18
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-2}=\frac{-12}{-4}
=+3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-2}=\frac{12}{-4}
=-3
$